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Infinite Soluble Groups

  • Chapter
A Course in the Theory of Groups

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 80))

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Abstract

The theory of infinite soluble groups has developed in directions quite different from the older theory of finite soluble groups. A noticeable feature of the infinite theory is the strong interaction with commutative algebra, which is due to the role played by the group ring. Despite this fact the exposition that follows is largely self-contained.

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Bibliography

Articles

  1. Asar, A.O., A conjugacy theorem for locally finite groups, J. London Math. Soc. (2) 6 (1973), 358–360.

    Article  MathSciNet  MATH  Google Scholar 

  2. Auslander, L., On a problem of Philip Hall, Ann. Math. (2) 86 (1967), 112–116.

    Article  MathSciNet  MATH  Google Scholar 

  3. Ayoub, C, On properties possessed by solvable and nilpotent groups, J. Austral. Math. Soc. 9 (1969), 218–227.

    Article  MathSciNet  MATH  Google Scholar 

  4. Baer, R., The subgroup of the elements of finite order of an abelian group, Ann. Math. 37 (1936), 766–781.

    Article  MathSciNet  Google Scholar 

  5. Baer, R., Nilpotent groups and their generalizations, Trans. Amer. Math. Soc. 47 (1940), 393–434.

    Article  MathSciNet  Google Scholar 

  6. Baer, R., Representations of groups as quotient groups, Trans. Amer. Math. Soc. 58 (1945), 295–419.

    MathSciNet  MATH  Google Scholar 

  7. Baer, R., Finiteness properties of groups, Duke Math. J. 15 (1948), 1021–1032.

    Article  MathSciNet  MATH  Google Scholar 

  8. Baer, R., Groups with descending chain condition for normal subgroups, Duke Math. J. 16, (1949), 1–22.

    Article  MathSciNet  MATH  Google Scholar 

  9. Baer, R., Endlichkeitskriterien für Kommutatorgruppen, Math. Ann. 124 (1952), 161–177.

    Article  MathSciNet  MATH  Google Scholar 

  10. Baer, R., Nilgruppen, Math. Z. 62 (1955), 402–437.

    Article  MathSciNet  MATH  Google Scholar 

  11. Baer, R., Classes of finite groups and their properties, Illinois J. Math. 1 (1957), 115–187.

    MathSciNet  MATH  Google Scholar 

  12. Baer, R., Engelsche Elemente Noetherscher Gruppen, Math. Ann. 133 (1957), 256–270.

    Article  MathSciNet  MATH  Google Scholar 

  13. Baer, R., Abzählbar erkennbare gruppentheoretische Eigenschaften, Math. Z. 79 (1962), 344–363.

    Article  MathSciNet  MATH  Google Scholar 

  14. Baer, R., Polyminimaxgruppen, Math. Ann. 175 (1968), 1–43. 479

    Article  MathSciNet  MATH  Google Scholar 

  15. Baer, R. and Levi, F., Freie Produkte und ihre Untergruppen, Compositio Math. 3 (1936), 391–398.

    MathSciNet  MATH  Google Scholar 

  16. Baumslag, G., Automorphism groups of residually finite groups, J. London Math. Soc. 38 (1963), 117–118.

    Article  MathSciNet  MATH  Google Scholar 

  17. Bender, H., A group theoretic proof of Burnside’s p a q b-theorem, Math. Z. 126 (1972), 327–338.

    Article  MathSciNet  MATH  Google Scholar 

  18. Birkhoff, G., On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31 (1935), 433–454.

    Article  Google Scholar 

  19. Burnside, W., On some properties of groups of odd order II, Proc. London Math. Soc. 33 (1901), 257–268.

    Article  MathSciNet  MATH  Google Scholar 

  20. Burnside, W., On an unsettled question in the theory of discontinuous groups, Quart. J. Pure Appl. Math. 33 (1902), 230–238.

    MATH  Google Scholar 

  21. Burnside, W., On groups of order pαqβ, Proc. London Math. Soc. (2) 1 (1904), 388–392.

    Article  MATH  Google Scholar 

  22. Cameron, P.J., Finite permutation groups and finite simple groups, Bull. London Math. Soc. 13 (1981), 1–22.

    Article  MathSciNet  MATH  Google Scholar 

  23. Čarin, V.S., *A remark on the minimal condition for subgroups, Dokl. Akad. Nauk. SSSR 66 (1949), 575–576.

    Google Scholar 

  24. Carin, V.S., *On soluble groups of type A3, Mat. Sb. 54 (1961), 489–499.

    MathSciNet  Google Scholar 

  25. Carter, R.W., Splitting properties of soluble groups, J. London Math. Soc. 36 (1961), 89–94.

    Article  MathSciNet  MATH  Google Scholar 

  26. Carter, R.W., Nilpotent self-normalizing subgroups of soluble groups, Math.Z. 75 (1961), 136–139.

    Article  MathSciNet  MATH  Google Scholar 

  27. Carter, R.W. and Hawkes, T.O., The ℱ-normalizers of a finite soluble group, J. Algebra 5 (1967), 176–202.

    Article  MathSciNet  Google Scholar 

  28. Černikov, S.N., *Infmite locally soluble groups, Mat. Sb. 7 (1940), 35–64.

    Google Scholar 

  29. Černikov, S.N., *On special p-groups, Mat. Sb. 27 (1950), 185–200.

    Google Scholar 

  30. Černikov, S.N., *Infmite groups with finite layers, Mat. Sb. 22 (1948), 101–133 Amer. Math. Soc. Translations (1) 56 (1951), 51-102.

    Google Scholar 

  31. Černikov, S.N., *On groups with finite classes of conjugate elements, Dokl. Akad. Nauk SSSR 114 (1957), 1177–1179.

    MathSciNet  Google Scholar 

  32. Černikov, S.N., *On layer-finite groups, Mat. Sb. 45 (1958), 415–416.

    MathSciNet  Google Scholar 

  33. Černikov, S.N., *Finiteness conditions in the general theory of groups, Uspehi Mat. Nauk 14 (1959), 45–96 = Amer. Math. Soc. Translations (2) 84 (1969), 1-67.

    MathSciNet  Google Scholar 

  34. Chevalley, C. Sur certains groupes simples, Tôhuku Math. J. (2) 7 (1955), 14–66.

    Article  MathSciNet  MATH  Google Scholar 

  35. Clifford, A.H., Representations induced in an invariant subgroup, Ann. Math. 38 (1937), 533–550.

    Article  MathSciNet  MATH  Google Scholar 

  36. Cooper, C.D.H., Power automorphisms of a group, Math. Z. 107 (1968), 335–356.

    Article  MathSciNet  MATH  Google Scholar 

  37. Čunihin, S.A., *On theorems of Sylow’s type, Dokl. Akad. Nauk. SSSR 66 (1949), 165–168.

    Google Scholar 

  38. Dedekind, R., Über Gruppen, deren sämtliche Teiler Normalteiler sind., Math. Ann. 48 (1897), 548–561.

    Article  MathSciNet  MATH  Google Scholar 

  39. Dicman, A.P., *On p-groups, Dokl. Akad. Nauk. SSSR 15 (1937), 71–76.

    MATH  Google Scholar 

  40. Dicman, A.P., Kuroš, A.G. and Uzkov, A.I., Sylowsche Untergruppen von unendlichen Gruppen, Mat. Sb. 3 (1938), 178–185.

    Google Scholar 

  41. Doerk, K., Minimal nicht überauflösbare, endliche Gruppen, Math. Z. 91 (1966), 198–205.

    Article  MathSciNet  Google Scholar 

  42. Durban, J.R., Residually central elements in groups, J. Algebra 9 (1968), 408–413.

    Article  MathSciNet  Google Scholar 

  43. Dyer, J.L. and Formanek, E., The automorphism group of a free group is complete, J. London Math. Soc. (2) 11 (1975), 181–190.

    Article  MathSciNet  MATH  Google Scholar 

  44. Eilenberg, S. and MacLane, S., Cohoraology theory in abstract groups I, II, Ann. Math. (2) 48 (1947), 51–78, 326-341.

    Article  MathSciNet  MATH  Google Scholar 

  45. Feit, W., The current situation in the theory of finite simple groups, Actes Congrès Intern. Math. (Nice 1970), Vol. 1, 55–93.

    Google Scholar 

  46. Feit, W. and Thompson, J.G., Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775–1029.

    Article  MathSciNet  MATH  Google Scholar 

  47. Fischer, B., Gaschütz, W., and Hartley, B., Injektoren endlicher auflösbarer Gruppen, Math. Z. 102 (1967), 337–339.

    Article  MathSciNet  MATH  Google Scholar 

  48. Fitting, H., Beiträge zur Theorie der Gruppen endlicher Ordnung, Jahresber. Deutsch. Math. Verein 48 (1938), 77–141.

    Google Scholar 

  49. Frattini, G., Intorno alla generazione dei gruppi di operazioni, Rend. Atti. Accad. Lincei (4) 1 (1885), 281–285, 455-457.

    MATH  Google Scholar 

  50. Frobenius, G., Ueber Relationen zwischen den Charakteren einer Gruppe und denen ihrer Untergruppen, Berliner Berichte (1898), 501–515.

    Google Scholar 

  51. Frobenius, G., Über auflösbare Gruppen V, S.-B. Preuss, Akad. Berlin (1901). 1324–1329.

    Google Scholar 

  52. Frobenius, G. and Stickelberger, L., öber Gruppen von vertauschbaren Elementen, J. Reine Angew. Math. 86 (1879), 217–262.

    Google Scholar 

  53. Gallian, J.A., The search for finite simple groups, Math. Mag. 49 (1976), 163–180.

    Article  MathSciNet  MATH  Google Scholar 

  54. Gaschütz, W., Zur Erweiterungstheorie endlicher Gruppen, J. Reine Angew. Math. 190 (1952), 93–107.

    MathSciNet  MATH  Google Scholar 

  55. Gaschütz, W., Über die Ф-Untergruppe endlicher Gruppen, Math. Z. 58 (1953), 160–170.

    Article  MathSciNet  MATH  Google Scholar 

  56. Gaschütz, W., Gruppen, in denen das Normalteilersein transitiv ist, J. Reine Angew. Math. 198 (1957), 87–92.

    MathSciNet  MATH  Google Scholar 

  57. Gaschütz, W., Zur Theorie der endlichen auflösbaren Gruppen, Math. Z. 80 (1963), 300–305.

    Article  MathSciNet  MATH  Google Scholar 

  58. Gaschütz, W., Nichtabelsche p-Gruppen besitzen äussere p-Automorphismen, J. Algebra 4 (1966), 1–2.

    Article  MathSciNet  MATH  Google Scholar 

  59. Golod, E.S., *On nil-algebras and residually finite p-groups, Izv. Akad Nauk SSSR Ser. Mat. 28 (1964), 273–276 = Amer. Math. Soc. Translations (2)48(1965), 103-106.

    MathSciNet  Google Scholar 

  60. Gorčakov, Yu.M, *On locally normal groups, Mat. Sb. 67 (1965), 244–254.

    MathSciNet  Google Scholar 

  61. Grigorčuk, R.I., *Burnside’s problem on periodic groups, Funktsional. Anal, i Prilozhen. 14 (1980), 53–54.

    MathSciNet  Google Scholar 

  62. Gruenberg, K.W., Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62.

    Article  MathSciNet  MATH  Google Scholar 

  63. Gruenberg, K.W., The Engel elements of a soluble group, Illinois J. Math. 3 (1959), 151–168.

    MathSciNet  MATH  Google Scholar 

  64. Gruenberg, K.W., The upper central series in soluble groups, Illinois J. Math. 5 (1961), 436–466.

    MathSciNet  MATH  Google Scholar 

  65. Grün, O., Beiträge zur Gruppentheorie I, J. Reine Angew. Math. 174 (1935), 1–14.

    Google Scholar 

  66. Gupta, N.D. and Sidki, S., On the Burnside problem for periodic groups, Math. Z. 182 (1983), 385–388.

    Article  MathSciNet  MATH  Google Scholar 

  67. Hall, P., A note on soluble groups, J. London Math. Soc. 3 (1928), 98–105.

    Article  MATH  Google Scholar 

  68. Hall, P., A contribution to the theory of groups of prime-power order, Proc. London Math. Soc. (2) 36 (1934), 29–95.

    Article  Google Scholar 

  69. Hall, P., A characteristic property of soluble groups, J. London Math. Soc. 12 (1937), 198–200.

    Article  Google Scholar 

  70. Hall, P., On the Sylow systems of a soluble group, Proc. London Math. Soc. (2), 43 (1937), 316–323.

    Google Scholar 

  71. Hall, P., On the system normalizers of a soluble group, Proc. London Math. Soc. (2) 43 (1937), 507–528.

    Google Scholar 

  72. Hall, P., Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436.

    Article  MathSciNet  MATH  Google Scholar 

  73. Hall, P., Theorems like Sylow’s, Proc. London Math. Soc. (3) 6 (1956), 286–304.

    Article  MathSciNet  MATH  Google Scholar 

  74. Hall, P., Finite-by-nilpotent groups, Proc. Cambridge Philos. Soc. 52 (1956), 611–616.

    Article  MathSciNet  MATH  Google Scholar 

  75. Hall, P., Some sufficient conditions for a group to be nilpotent, Illinois J. Math. 2 (1958), 787–801.

    MathSciNet  MATH  Google Scholar 

  76. Hall, P., Periodic FC-groups, J. London Math. Soc. 34 (1959), 289–304.

    Article  MathSciNet  MATH  Google Scholar 

  77. Hall, P., On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595–622.

    Article  MathSciNet  MATH  Google Scholar 

  78. Hall, P., The Frattini subgroups of finitely generated groups, Proc. London Math. Soc. (3) 11 (1961), 327–352.

    Article  MathSciNet  MATH  Google Scholar 

  79. Hall, P., On non-strictly simple groups, Proc. Cambridge Philos. Soc. 59 (1963), 531–553.

    Article  MathSciNet  MATH  Google Scholar 

  80. Hall, P. and Higman, G., On the p-length of p-soluble groups and reduction theorems for Burnside’s problem, Proc. London Math. Soc. (3) 6 (1956), 1–42.

    Article  MathSciNet  MATH  Google Scholar 

  81. Hall, P. and Kulatilaka, C.R., A property of locally finite groups, J. London Math. Soc. 39 (1964), 235–239.

    Article  MathSciNet  MATH  Google Scholar 

  82. Hartley, B., The residual nilpotence of wreath products, Proc. London Math. Soc. (3) 20 (1970), 365–392.

    Article  MathSciNet  MATH  Google Scholar 

  83. Hartley, B., A note on the normalizer condition, Proc. Cambridge Philos. Soc. 74 (1973), 11–15.

    Article  MathSciNet  MATH  Google Scholar 

  84. Hawkes, T.O., On formation subgroups of a finite soluble group, J. London Math. Soc. 44 (1969), 243–250.

    Article  MathSciNet  MATH  Google Scholar 

  85. Head, T.J., Note on the occurrence of direct factors in groups, Proc. Amer. Math. Soc. 15 (1964), 193–195.

    Article  MathSciNet  MATH  Google Scholar 

  86. Heineken, H., Eine Bemerkung über engelsche Elemente, Arch. Math. (Basel) 11 (1960), 321.

    Article  MathSciNet  MATH  Google Scholar 

  87. Heineken, H., Engelsche Elemente der Länge drei, Illinois J. Math. 5 (1961), 681–707.

    MathSciNet  MATH  Google Scholar 

  88. Heineken, H. and Mohamed, I.J., A group with trivial centre satisfying the normalizer condition, J. Algebra 10 (1968), 368–376.

    Article  MathSciNet  MATH  Google Scholar 

  89. Higman, G., The units of group-rings, Proc. London Math. Soc. (2) 46 (1940), 231–248.

    Article  MathSciNet  Google Scholar 

  90. Higman, G., A finitely generated infinite simple group, J. London Math. Soc. 26 (1951), 61–64.

    Article  MathSciNet  MATH  Google Scholar 

  91. Higman, G., Complementation of abelian normal subgroups, Publ. Math. Debrecen 4 (1956), 455–458.

    MathSciNet  MATH  Google Scholar 

  92. Higman, G., Subgroups of finitely presented groups, Proc. Roy. Soc. London Ser. A262 (1961), 455–475.

    Article  MathSciNet  Google Scholar 

  93. Higman, G., Neumann, B.H., and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247–254.

    Article  MathSciNet  Google Scholar 

  94. Hirsch, K.A., On infinite soluble groups I, Proc. London Math. Soc. (2) 44 (1938), 53–60.

    Article  Google Scholar 

  95. Hirsch, K.A., On infinite soluble groups II, Proc. London Math. Soc. (2) 44 (1938), 336–344.

    Article  MATH  Google Scholar 

  96. Hirsch, K.A., On infinite soluble groups III, Proc. London Math. Soc. (2) 49 (1946), 184–194.

    Article  MathSciNet  MATH  Google Scholar 

  97. Hirsch, K.A., On infinite soluble groups IV, J. London Math. Soc. 27 (1952), 81–85.

    Article  MathSciNet  MATH  Google Scholar 

  98. Hirsch, K.A., On infinite soluble groups V, J. London Math. Soc. 29 (1954), 250–251.

    Article  MathSciNet  MATH  Google Scholar 

  99. Hirsch, K.A., Über lokal-nilpotente Gruppen, Math. Z. 63 (1955), 290–294.

    Article  MathSciNet  MATH  Google Scholar 

  100. Hölder, O., Bildung zusammengesetzer Gruppen, Math. Ann 46 (1895), 321–422.

    Article  MathSciNet  MATH  Google Scholar 

  101. Hopf, H., Über die Bettischen Gruppen, die zu einer beliebigen Gruppe gehören, Comment. Math. Helv. 17 (1944/45), 39–79.

    Article  MathSciNet  Google Scholar 

  102. Hulse, J. A., Automorphism towers of polycyclic groups, J. Algebra 16 (1970), 347–398.

    Article  MathSciNet  MATH  Google Scholar 

  103. Huppert, B., Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z. 60 (1954), 409–434.

    Article  MathSciNet  MATH  Google Scholar 

  104. Itô, N., Note on S-groups, Proc. Japan Acad. 29 (1953), 149–150.

    Article  MathSciNet  MATH  Google Scholar 

  105. Iwasawa, K., Über die endlichen Gruppen und die Verbände ihrer Untergruppen, J. Univ. Tokyo 4 (1941), 171–199.

    MathSciNet  MATH  Google Scholar 

  106. Iwasawa, K., Einige Sätze über freie Gruppen, Proc. Imp. Acad. Tokyo 19 (1943), 272–274.

    Article  MathSciNet  MATH  Google Scholar 

  107. Jategaonkar. A.V., Integral group rings of polycyclic-by-finite groups, J. Pure Appl. Algebra 4 (1974), 337–343.

    Article  MathSciNet  MATH  Google Scholar 

  108. Jordan, C, Recherches sur les substitutions, J. Math. Pure Appl. (2) 17 (1872), 351–363.

    Google Scholar 

  109. Kalužnin, L.A., Über gewisse Beziehungen zwischen einer Gruppe und ihren Automorphismen, Berlin Math. Tagung (1953), 164–172.

    Google Scholar 

  110. Kalužnin, L. and Krasner, M., Produit complet des groupes de permutations et problème d’extension des groupes, Acta Sci. Math. Szeged. 13 (1950), 208–230, 14 (1951), 39-66, 69-82.

    MathSciNet  Google Scholar 

  111. Kappe, L.-C. and Kappe, W.P., On three-Engel groups, Bull. Austral. Math. Soc. 7 (1972), 391–405.

    Article  MathSciNet  MATH  Google Scholar 

  112. Kargapolov, M.I., *On a problem of O. Yu Schmidt, Sibirsk Math. Z. 4 (1963), 232–235.

    MathSciNet  MATH  Google Scholar 

  113. Kegel, O.H., Produkte nilpotenter Gruppen, Arch. Math. (Basel) 12 (1961), 90–93.

    Article  MathSciNet  MATH  Google Scholar 

  114. Kegel, O.H., Noethersche 2-Gruppen sind endlich, Monatsh. Math. 71 (1967), 424–426.

    Article  MathSciNet  MATH  Google Scholar 

  115. Kegel, O.H. and Wehrfritz, B.A.F., Strong finiteness conditions in locally finite groups, Math. Z. 117 (1970), 309–324.

    Article  MathSciNet  MATH  Google Scholar 

  116. Kolchin, E.R., On certain concepts in the theory of algebraic matric groups, Ann. Math. (2) 49 (1948), 774–789.

    Article  MathSciNet  MATH  Google Scholar 

  117. Kostrikin, A.I., *The Burnside problem, Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 3–34.

    MathSciNet  MATH  Google Scholar 

  118. Krull, W., Über verallgemeinerte endliche Abelsche Gruppen, Math. Ann. 23 (1925), 161–196.

    MathSciNet  MATH  Google Scholar 

  119. Kulikov, L.Ya, *On the theory of abelian groups of arbitrary cardinality, Mat. Sb. 9 (1941), 165–182.

    Google Scholar 

  120. Kulikov, L.Ya, *On the theory of abelian groups of arbitrary power, Mat. Sb. 16 (1945), 129–162.

    Google Scholar 

  121. Kuroš, A.G., Die Untergruppen der freien Produkte von beliebigen Gruppen, Math. Ann. 109 (1934), 647–660.

    Article  MathSciNet  Google Scholar 

  122. Kuroš, A.G. and Černikov, S.N., *Soluble and nilpotent groups, Uspehi Mat. Nauk 2 (1947), 18–59 Amer. Math. Soc. Translations 80 (1953).

    Google Scholar 

  123. Lennox, J.C. and Roseblade, J.E., Centrality in finitely generated soluble groups, J. Algebra 16 (1970), 399–435.

    Article  MathSciNet  MATH  Google Scholar 

  124. Levi, F.W., Groups in which the commutator operation satisfies certain algebraic conditions, J. Indian Math. Soc. 6 (1942), 87–97.

    MathSciNet  MATH  Google Scholar 

  125. Levi, F.W. and van der Waerden, B.L., Über eine besondere Klasse von Gruppen, Abh. Math. Sent. Univ. Hamburg 9 (1932), 154–158.

    Article  Google Scholar 

  126. Lyndon, R.C., The cohomology theory of group extensions, Duke Math. J. 15 (1948), 271–292.

    Article  MathSciNet  MATH  Google Scholar 

  127. MacLane, S., Cohomology theory in abstract groups III, Ann. Math. (2) 50 (1949), 736–761.

    Article  MathSciNet  MATH  Google Scholar 

  128. MacLane, S., A proof of the subgroup theorem for free products, Mathematika 5 (1958), 13–19.

    Article  MathSciNet  MATH  Google Scholar 

  129. Magnus, W., Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), 259–280.

    Article  MathSciNet  Google Scholar 

  130. Magnus, W., Über freie Faktorgruppen und freie Untergruppen gegebener Gruppen, Monatsh. Math. Phys. 47 (1939), 307–313.

    Article  MathSciNet  Google Scholar 

  131. Mal’cev, A.I., *On the faithful representation of infinite groups by matrices, Mat. Sb. 8 (1940), 405–422 = Amer. Math. Soc. Translations (2) 45 (1965), 1-18.

    MathSciNet  MATH  Google Scholar 

  132. Mal’cev, A.I., *On a general method of obtaining local theorems in group theory, Ivanov. Gos. Ped. Inst. Učen. Zap. 1 (1941), 3–9.

    MathSciNet  Google Scholar 

  133. Mal’cev, A.I., *Generalized nilpotent algebras and their adjoint groups, Mat. Sb. 25 (1949), 347–366 = Amer. Math. Soc. Translations (2) 69 (1968), 1-21.

    MathSciNet  Google Scholar 

  134. Mal’cev, A.I., *On certain classes of infinite soluble groups, Math. Sb. 28 (1951), 567–588 = Amer. Math. Soc. Translations (2) 2 (1956), 1-21.

    MathSciNet  Google Scholar 

  135. Mal’cev, A.I., *Homomorphisms of finite groups, Ivanov Gos. Ped. Inst. Učen. Zap. 18 (1958), 49–60.

    Google Scholar 

  136. Mathieu, E., Mémoire sur l’etude des fonctions de plusieur quantites, J. Math. Pures Appl. (2) 6 (1861), 241–323.

    MathSciNet  Google Scholar 

  137. Mathieu, E., Sur la fonction cinq fois transitive de 24 quantités, J. Math. Pures Appl. (2) 18 (1873), 25–46.

    Google Scholar 

  138. McLain, D.H., A characteristically-simple group, Proc. Cambridge Philos. Soc. 50 (1954), 641–642.

    Article  MathSciNet  MATH  Google Scholar 

  139. McLain, D.H., On locally nilpotent groups, Proc. Cambridge Philos. Soc. 52 (1956), 5–11.

    Article  MathSciNet  MATH  Google Scholar 

  140. McLain, D.H., Finiteness conditions in locally soluble groups, J. London Math. Soc. 34 (1959), 101–107.

    Article  MathSciNet  MATH  Google Scholar 

  141. Meldrum, J.D.P., On the Heineken—Mohamed groups, J. Algebra 27 (1973), 437–444.

    Article  MathSciNet  MATH  Google Scholar 

  142. Neumann, B.H., Identical relations in groups I, rMath. Ann. 114 (1937), 506–525.

    Article  Google Scholar 

  143. Neumann, B.H., Groups with finite classes of conjugate elements, Proc. London Math. Soc. (3) 1 (1951), 178–187.

    Article  MathSciNet  MATH  Google Scholar 

  144. Neumann, B.H., An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. A 246 (1954), 503–554.

    Article  MATH  Google Scholar 

  145. Neumann, B.H. and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 34 (1959), 465–479.

    Article  MathSciNet  MATH  Google Scholar 

  146. Newman, M.F., On a class of nilpotent groups, Proc. London Math. Soc. (3) 10 (1960), 365–375.

    Article  MathSciNet  MATH  Google Scholar 

  147. Newman, M.F., The soluble length of soluble linear groups, Math. Z. 126 (1972), 59–70.

    Article  MathSciNet  MATH  Google Scholar 

  148. Newman, M.F., Problems, in “Burnside Groups”, Lecture Notes in Math. Vol. 806, Springer-Verlag, Berlin (1980), 249–254.

    Google Scholar 

  149. Nielsen, J., Om Regning med ikke kommutative Faktoren og dens Anvendelse i Gruppeteorien, Mat. Tidssk. B (1921), 77–94.

    Google Scholar 

  150. Novikov, P.S. and Adjan, S.I., *Infinite periodic groups, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 212–244, 251-524, 709-731 = Math. VSSR-Izv 2 (1968) 209-236, 241-479, 665-685.

    MathSciNet  Google Scholar 

  151. Novikov, P.S. and Adjan, S.I., *Commutative subgroups and the conjugacy problem in free periodic groups of odd order, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 1176–1190 = Math. USSR-Izv. 2 (1968), 1131-1144.

    MathSciNet  MATH  Google Scholar 

  152. Ol’sanskii, A.Yu, *An infinite group with subgroups of prime orders, Izv. Akad. Nauk. SSSR Ser. Mat. 44 (1980), 309–321.

    MathSciNet  Google Scholar 

  153. Peng, T.A., Engel elements of groups with maximal condition on abelian subgroups. Nanta Math. 1 (1966), 23–28.

    MathSciNet  Google Scholar 

  154. Peng, T.A., Finite groups with pro-normal subgroups, Proc. Amer. Math. Soc. 20 (1969), 232–234.

    Article  MathSciNet  MATH  Google Scholar 

  155. Phillips, R.E. and Roseblade, J.E., A residually central group that is not a Z-group, Michigan Math. J. 25 (1978), 233–234.

    Article  MathSciNet  MATH  Google Scholar 

  156. Plotkin, B.I., *On some criteria of locally nilpotent groups, Uspehi Mat. Nauk 9 (1954), 181–186 = Amer. Math. Soc. Translations (2) 17 (1961), 1-7.

    MathSciNet  MATH  Google Scholar 

  157. Plotkin, B.I., *Radical groups, Mat. Sb. 37 (1955), 507–526 = Amer. Math. Soc. Translations (2) 17 (1961), 9-28.

    MathSciNet  Google Scholar 

  158. Plotkin, B.I., *Generalized soluble and nilpotent groups, Uspehi Mat. Nauk 13 (1958), 89–172 = Amer. Math. Soc. Translations (2) 17 (1961), 29–115.

    MathSciNet  MATH  Google Scholar 

  159. Polovickii, Ya.D., *Layer-extremal groups, Mat. Sb. 56 (1962), 95–106.

    MathSciNet  Google Scholar 

  160. Prüfer, H., Untersuchungen über die Zerlegbarkeit der abzählbaren primären Abelschen Gruppen, Math. Z. 17 (1923), 35–61.

    Article  MathSciNet  MATH  Google Scholar 

  161. Rae, A. and Roseblade, J.E., Automorphism towers of extremal groups, Math. Z. 117 (1970), 70–75.

    Article  MathSciNet  MATH  Google Scholar 

  162. Razmyslov, Yu.P., The Hall—Higman Problem, Izv. Akad. Nauk. SSSR Ser. Mat. 42 (1978), 833–867.

    MathSciNet  MATH  Google Scholar 

  163. Remak, R., Über die Zerlegung der endlichen Gruppen in direkte unzerlegbare Faktoren, J. Reine Angew. Math. 139 (1911), 293–308.

    MATH  Google Scholar 

  164. Remak, R., Über minimale invariante Untergruppen in der Theorie der endlichen Gruppen, J. Reine Angew. Math. 162 (1930), 1–16.

    MATH  Google Scholar 

  165. Remak, R., Über die Darstellung der endlichen Gruppen als Untergruppen direkter Produkte, J. Reine Angew. Math. 163 (1930), 1–44.

    MATH  Google Scholar 

  166. Robinson, D.J.S., Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc. 60 (1964), 21–38.

    Article  MathSciNet  MATH  Google Scholar 

  167. Robinson, D.J.S., Joins of subnormal subgroups, Illinois J. Math. 9 (1965), 144–168.

    MathSciNet  MATH  Google Scholar 

  168. Robinson, D.J.S., On the theory of subnormal subgroups, Math. Z. 89 (1965), 30–51.

    Article  MathSciNet  MATH  Google Scholar 

  169. Robinson, D.J.S., A note on finite groups in which normality is transitive, Proc. Amer. Math. Soc. 19 (1968), 933–937.

    Article  MathSciNet  MATH  Google Scholar 

  170. Robinson, D.J.S., Hypercentral ideals, noetherian modules and a theorem of Stroud, J. Algebra 32 (1974), 234–239.

    Article  MathSciNet  MATH  Google Scholar 

  171. Robinson, D.J.S., A new treatment of soluble groups with finiteness conditions on their abelian subgroups, Bull. London Math. Soc. 8 (1976), 113–129.

    Article  MathSciNet  MATH  Google Scholar 

  172. Robinson, D.J.S., Recent results on finite complete groups, in Algebra Carbondale 1980, Lecture Notes in Math. Vol. 848, Springer-Verlag, Berlin (1981), 178–185.

    Google Scholar 

  173. Roseblade, J.E., On certain subnormal coalition classes, J. Algebra 1 (1964), 132–138.

    Article  MathSciNet  MATH  Google Scholar 

  174. Roseblade, J.E, On groups in which every subgroup is subnormal, J. Algebra 2 (1965), 402–412.

    Article  MathSciNet  MATH  Google Scholar 

  175. Roseblade, J.E., The permutability of orthogonal subnormal subgroups, Math. Z. 90 (1965), 365–372.

    Article  MathSciNet  MATH  Google Scholar 

  176. Roseblade, J.E., A note on subnormal coalition classes, Math. Z. 90 (1965), 373–375.

    Article  MathSciNet  MATH  Google Scholar 

  177. Roseblade, J.E., The derived series of a join of subnormal subgroups, Math. Z. 117 (1970), 57–69.

    Article  MathSciNet  MATH  Google Scholar 

  178. Roseblade, J.E., The integral group rings of hypercentral groups, Bull. London Math. Soc. 3 (1971), 351–355.

    Article  MathSciNet  MATH  Google Scholar 

  179. Roseblade. J.E., Group rings of polycyclic groups, J. Pure Appl. Algebra 3 (1973), 307–321.

    Article  MathSciNet  MATH  Google Scholar 

  180. Roseblade, J.E., Applications of the Artin-Rees lemma to group rings, Symposia Math. 17 (1976), 471–478.

    MathSciNet  Google Scholar 

  181. Roseblade, J.E. and Stonehewer, S.E., Subjunctive and locally coalescent classes of groups, J. Algebra 8 (1968), 423–435.

    Article  MathSciNet  MATH  Google Scholar 

  182. Sanov, I.N., *Solution of Burnside’s problem for exponent 4, Leningrad State Univ. Annals Učen. Zap.) Mat. Ser. 10 (1940), 166–170.

    MathSciNet  Google Scholar 

  183. Schenkman, E., The splitting of certain solvable groups, Proc. Amer. Math. Soc. 6 (1955), 286–290.

    Article  MathSciNet  MATH  Google Scholar 

  184. Schenkman, E., On the norm of a group, Illinois J. Math. 4 (1960), 150–152.

    MathSciNet  MATH  Google Scholar 

  185. Schmid, P., Every saturated formation is a local formation, J. Algebra 51 (1978), 144–148.

    Article  MathSciNet  MATH  Google Scholar 

  186. Schmidt, O.J., Sur les produits directs, Bull. Soc. Math. France 41 (1913), 161–164.

    MathSciNet  MATH  Google Scholar 

  187. Schmidt, O.J., Über Gruppen, deren sämtliche Teiler spezielle Gruppen sind, Rec. Math. Moscow 31 (1924), 366–372.

    Google Scholar 

  188. Schmidt, O.J., *Infinite soluble groups, Mat Sb. 17 (1945), 145–162.

    Google Scholar 

  189. Schmidt, O.J., *The local finiteness of a class of periodic groups, Ivbr. Trudi (1959), 298–300, German translation Math. Forschungsberichte Bd. 20 (1973), 79-81.

    Google Scholar 

  190. Schreier, O., Über die Erweiterung von Gruppen I, Monatsh. Math. Phys. 34 (1926), 165–180.

    Article  MathSciNet  MATH  Google Scholar 

  191. Schreier, O., Über die Erweiterung von Gruppen II, Abh. Math. Sent. Univ. Hamburg 4 (1926), 321–346.

    Article  Google Scholar 

  192. Schreier, O., Die Untergruppen der freien Gruppen, Abh. Math. Sem. Univ. Hamburg 5 (1927), 161–183. [a193] Schur, I., Neuer Beweis eines Satzes über endliche Gruppen, S.-B. Preuss Akad. Berlin (1902), 1013–1019.

    Article  MATH  Google Scholar 

  193. Schur, I., Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 127 (1904), 20–50.

    MATH  Google Scholar 

  194. Schur, I., Untersuchungen über die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Regine Angew. Math. 132 (1907), 85–137.

    MATH  Google Scholar 

  195. Seksenbaev, K., *On the theory of polycyclic groups. Algebra i Logika 4 (1965), 79–83.

    MathSciNet  MATH  Google Scholar 

  196. Šmelkin, A.L., *Polycylic groups, Sibirsk. Mat. Ž. 9 (1968), 234–235 = Siberian Math. J. 9 (1968), 178.

    MathSciNet  Google Scholar 

  197. Specker, E., Additive Gruppen von Folgen ganzer Zahlen, Portugal. Math. 9 (1950), 131–140.

    MathSciNet  MATH  Google Scholar 

  198. Stewart, A.G.R., On the class of certain nilpotent groups, Proc. Roy. Soc. London Ser. A 292 (1966), 374–379.

    Article  MATH  Google Scholar 

  199. Stonehewer, S.E., The join of finitely many subnormal subgroups, Bull. London Math. Soc. 2 (1970), 77–82.

    Article  MathSciNet  MATH  Google Scholar 

  200. Stonehewer, S.E., Permutable subgroups of infinite groups, Math. Z. 125 (1972), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  201. Strebel, R., Finitely presented soluble groups, in Group Theory, Essays for Philip Hall, Cambridge University Press, Cambridge (1984).

    Google Scholar 

  202. Sunkov, V.P., *On locally finite groups with a minimality condition for abelian subgroups, Algebra i Logika 9 (1970), 579–615 = Algebra and Logic 9 (dy1970), 350-370.

    MathSciNet  Google Scholar 

  203. Šunkov, V.P., *Locally finite groups of finite rank, Algebra i Logika 10 (1971), 199–225 = Algebra and Logic 10 (1971), 127-142.

    MathSciNet  Google Scholar 

  204. Swan, R.G., Representations of polycyclic groups, Proc. Amer. Math. Soc. 18 (1967), 573–574.

    MathSciNet  MATH  Google Scholar 

  205. Sylow, L., Théorèmes sur les groupes de substitutions, Math. Ann. 5 (1872), 584–594.

    Article  MathSciNet  MATH  Google Scholar 

  206. Taunt, D., On A-groups, Proc. Cambridge Philos. Soc. 45 (1949), 24–42.

    Article  MathSciNet  MATH  Google Scholar 

  207. Thompson, J.G., Finite groups with fixed-point-free automorphisms of prime order, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 578–581.

    Article  MathSciNet  MATH  Google Scholar 

  208. Thompson, J.G., Normal p-complements for finite groups, J. Algebra 1 (1964), 43–46.

    Article  MathSciNet  MATH  Google Scholar 

  209. Ulm, H, Zur Theorie der abzählbar-unendlichen Abelschen Gruppen, Math. Ann. 107 (1933), 774–803.

    Article  MathSciNet  Google Scholar 

  210. Wehrfritz, B.A.F., Frattini subgroups in finitely generated linear groups, J. London Math. Soc. 43 (1968), 619–622.

    Article  MathSciNet  MATH  Google Scholar 

  211. Weir, A.J., The Reidemeister—Schreier and Kuroš Subgroup Theorems, Mathematika 3 (1956), 47–55.

    Article  MathSciNet  MATH  Google Scholar 

  212. Wiegold, J., Groups with boundedly finite classes of conjugate elements, Proc. Roy. Soc. London Ser. A 238 (1957), 389–401.

    Article  MathSciNet  MATH  Google Scholar 

  213. Wielandt, H., Eine Kennzeichnung der direkten Produkte von p-Gruppen, Math. Z. 41 (1936), 281–282.

    Article  MathSciNet  Google Scholar 

  214. Wielandt, H., Eine Verallgemeinerung der invarianten Untergruppen, Math. Z. 45 (1939), 209–244.

    Article  MathSciNet  Google Scholar 

  215. Wielandt, H., Zum Satz von Sylow, Math. Z. 60 (1954), 407–408.

    Article  MathSciNet  MATH  Google Scholar 

  216. Wielandt, H., Vertauschbare nachinvariante Untergruppen, Abh. Math. Sem. Univ. Hamburg 21 (1957), 55–62.

    Article  MathSciNet  MATH  Google Scholar 

  217. Wielandt, H., Über den Normalisator der subnormalen Untergruppen, Math. Z. 69 (1958), 463–465.

    Article  MathSciNet  MATH  Google Scholar 

  218. Wielandt, H., Über Produkte von nilpotenten Gruppen, Illinois J. Math. 2 (1958), 611–618.

    MathSciNet  MATH  Google Scholar 

  219. Wielandt, H., Über die Existenz von Normalteilern in endlichen Gruppen, Math. Nachr. 18 (1958), 274–280.

    Article  MathSciNet  MATH  Google Scholar 

  220. Wielandt, H., Über die Normalstruktur von mehrfach faktorisierbaren Gruppen, J. Austral. Math. Soc. 1 (1960), 143–146.

    Article  MathSciNet  MATH  Google Scholar 

  221. Wilson, J.S., Some properties of groups inherited by normal subgroups of finite index, Math. Z. 114 (1970), 19–21.

    Article  MathSciNet  MATH  Google Scholar 

  222. Wilson, J.S., On periodic generalized nilpotent groups, Bull. London Math. Soc. 9 (1977), 81–85.

    Article  MathSciNet  MATH  Google Scholar 

  223. Witt, E., Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg 12 (1938), 256–264.

    Article  Google Scholar 

  224. Wong, W.J., On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2, J. Austral. Math. Soc. 4 (1964), 90–112.

    Article  MathSciNet  MATH  Google Scholar 

  225. Zaičev, D.I., *On groups which satisfy a weak minimality condition, Mat. Sb. 78 (1969), 323–331 = Math. USSR Sb. 7 (1969), 315-322.

    MathSciNet  Google Scholar 

  226. Zappa, G., Sui gruppi di Hirsch supersolubili, Rend. Sem. Mat. Univ. Padova 12 (1941), 1–11, 62-80.

    MathSciNet  Google Scholar 

  227. Zassenhaus, H., Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamburg 11 (1936), 187–220.

    Article  Google Scholar 

  228. Zassenhaus, H., Beweis eines Satzes über diskrete Gruppen, Abh. Math. Sem. Univ. Hamburg 12 (1938), 289–312.

    Article  Google Scholar 

  229. Zorn, M., Nilpotency of finite groups, Bull. Amer. Math. Soc. 42 (1936), 485–486.

    Google Scholar 

Books

  1. Adjan, S.I., The Burnside Problem and Identities in Groups, translated from the Russian by J.C. Lennox and J. Wiegold, Springer-Verlag, Berlin (1978).

    Google Scholar 

  2. Aschbacher, M, Finite Group Theory, Cambridge University Press, New York (1986).

    MATH  Google Scholar 

  3. Atiyah, M.F. and Macdonald, I.G., Introduction to Commutative Algebra, Addison-Wesley, Reading, MA (1969).

    MATH  Google Scholar 

  4. Baumslag, G., Lecture Notes on Nilpotent Groups, American Mathematical Society, Providence, RI (1971).

    MATH  Google Scholar 

  5. Bieri, R., Homological Dimension of Discrete Groups, Queen Mary College Mathematics Notes, London (1976).

    Google Scholar 

  6. Blackburn, N. and Huppert, B., Finite Groups, Springer-Verlag, Berlin (1967–82).

    Google Scholar 

  7. Burnside, W., Theory of Groups of Finite Order, 2nd edn., Cambridge University Press, Cambridge (1911) (Dover reprint 1955).

    MATH  Google Scholar 

  8. Cartan, H. and Eilenberg, S., Homological Algebra, Princeton University Press, Princeton, NJ (1956).

    MATH  Google Scholar 

  9. Carter, R.W., Simple Groups of Lie Type, Wiley—Interscience, New York (1972).

    MATH  Google Scholar 

  10. Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A., ATLAS of Finite Groups, Oxford University Press, New York (1985).

    MATH  Google Scholar 

  11. Coxeter, H.S.M., Introduction to Geometry, Wiley, New York (1961).

    MATH  Google Scholar 

  12. Coxeter, H.S.M. and Moser, W.O.J., Generators and Relations for Discrete Groups, 3rd edn., Springer-Verlag, Berlin (1972).

    MATH  Google Scholar 

  13. Curtis, C.W., and Reiner, I., Methods of Representation Theory, Wiley, New York (1981).

    MATH  Google Scholar 

  14. Dickson, L.E., Linear Groups with an Exposition of the Galois Field Theory, Teubner, Leipzig (1901) (Dover reprint 1958).

    MATH  Google Scholar 

  15. Dixon, J.D., Problems in Group Theory, Blaisdell, Waltham, MA (1967).

    Google Scholar 

  16. Dixon, J.D., The Structure of Linear Groups, Van Nostrand, London (1971).

    MATH  Google Scholar 

  17. Dixon, J.D. and Puttaswamaiah, B.M., Modular Representations of Finite Groups, Academic Press, New York (1977).

    MATH  Google Scholar 

  18. Dixon, M.R., Sylow Theory, Formations and Fitting Classes in Locally Finite Groups, World Scientific, Singapore (1994).

    Book  MATH  Google Scholar 

  19. Doerk, K. and Hawkes, T.O., Finite Soluble Groups, de Gruyter, Berlin (1992).

    Google Scholar 

  20. Dornhoff, L., Group Representation Theory, 2 vols., Marcel Dekker, New York (1971).

    MATH  Google Scholar 

  21. Epstein, D.B.A., Word Processing in Groups, Jones and Bartlet, Boston (1992).

    Google Scholar 

  22. Feit, W., Characters of Finite Groups, Benjamin, New York (1967).

    MATH  Google Scholar 

  23. Fricke, R. and Klein, F., Vorlesungen über die Theorie der Elliptischen Modulfunktionen, 2 vols., Teubner, Leipzig (1890–2).

    Google Scholar 

  24. Fuchs, L., Abelian Groups, Pergamon, Oxford, UK (1960).

    MATH  Google Scholar 

  25. Fuchs, L., Infinite Abelian Groups, 2 vols., Academic_Press, New York (1970–3).

    MATH  Google Scholar 

  26. Gorenstein, D., Finite Groups, Harper & Row, New York (1968).

    MATH  Google Scholar 

  27. Gorenstein, D., Finite Simple Groups, Plenum Press, New York (1982).

    MATH  Google Scholar 

  28. Griffith, P.A., Infinite Abelian Group Theory, University of Chicago Press, Chicago (1970).

    MATH  Google Scholar 

  29. Gruenberg, K.W., Cohomological Topics in Group Theory, Lecture Notes in Math., vol. 143, Springer-Verlag, Berlin (1970).

    MATH  Google Scholar 

  30. Gupta, N.D., Burnside Groups and Related Topics, University of Manitoba, Winnipeg (1976).

    Google Scholar 

  31. Hall, M., The Theory of Groups, Macmillan, New York (1959).

    MATH  Google Scholar 

  32. Hall, P., The Edmonton Notes on Nilpotent Groups, Queen Mary College Mathematics Notes, London (1969).

    Google Scholar 

  33. Herstein, I.N., Topics in Ring Theory, University of Chicago Press, Chicago (1969).

    MATH  Google Scholar 

  34. Hilton, P.J. and Stammbach, U., A Course in Homological Algebra, Springer-Verlag, New York (1970).

    Google Scholar 

  35. Johnson, D.L., Presentations of Groups, London Mathematical Society Lecture Notes Series 22, Cambridge (1976).

    MATH  Google Scholar 

  36. Jordan, C, Traité des Substitutions et des Équations Algébriques, Gauthier-Villars (1870) (Blanchard reprint 1957).

    Google Scholar 

  37. Kaplansky, I., Infinite Abelian Groups, 2nd edn., University of Michigan Press, Ann Arbor, MI (1969).

    MATH  Google Scholar 

  38. Kargapolov, M.I. and Merzljakov, Ju.I, Fundamentals of the Theory of Groups, 2nd edn., translated from the Russian by R.G. Burns, Springer-Verlag, New York (1979).

    Chapter  Google Scholar 

  39. Kegel, O.H. and Wehrfritz, B.A.F., Locally Finite Groups, North-Holland, Amsterdam (1973).

    Google Scholar 

  40. Kuroš, A.G., The Theory of Groups, 2nd edn., 2 vols., translated from the Russian by K.A. Hirsch, Chelsea, New York (1960).

    Google Scholar 

  41. Kuroš, A.G., Gruppentheorie, 3rd edn., 2 vols., German translation, Akademie-Verlag, Berlin (1972).

    Google Scholar 

  42. Lennox, J.C. and Stonehewer, S.E., Subnormal Subgroups, Oxford University Press, New York (1987).

    MATH  Google Scholar 

  43. Lyndon, R.C. and Schupp, P.E., Combinatorial Group Theory, Springer-Verlag, Berlin (1977).

    MATH  Google Scholar 

  44. MacLane, S., Homology, Springer-Verlag, Berlin (1967).

    Google Scholar 

  45. Magnus, W., Karrass, A., and Solitar, D., Combinatorial Group Theory, Wiley—Interscience, New York (1966).

    MATH  Google Scholar 

  46. Miller, C.F. III, On Group Theoretic Decision Problems and Their Classification, Princeton University Press, Princeton, NJ (1971).

    MATH  Google Scholar 

  47. Neumann, B.H., Lectures on Topics in the Theory of Infinite Groups, Tata Institute, Bombay (1960).

    Google Scholar 

  48. Neumann, H., Varieties of Groups, Springer-Verlag, Berlin (1967).

    Book  MATH  Google Scholar 

  49. Passi, I.B.S., Group Rings and Their Augmentation Ideals, Lecture Notes in Math., Vol. 715, Springer-Verlag, Berlin (1979).

    MATH  Google Scholar 

  50. Passman, D.S., Permutation Groups, Benjamin, New York (1968).

    MATH  Google Scholar 

  51. Passman, D.S., The Algebraic Structure of Group Rings, Wiley—Interscience, New York (1977).

    MATH  Google Scholar 

  52. Plotkin, B.I., Groups of Automorphisms of Algebraic Systems, translated from the Russian by K.A. Hirsch, Wolters-Noordhoff, Groningen (1972).

    Google Scholar 

  53. Robinson, D.J.S., Infinite Soluble and Nilpotent Groups, Queen Mary College Mathematics Notes, London (1968).

    Google Scholar 

  54. Robinson, D.J.S., Finiteness Conditions and Generalized Soluble Groups, 2 vols., Springer-Verlag, Berlin (1972).

    Book  Google Scholar 

  55. Robinson, G. de B., Representation Theory of the Symmetric Group, Toronto (1961).

    Google Scholar 

  56. Rose, J.S., A Course on Group Theory, Cambridge University Press, Cambridge (1978).

    Google Scholar 

  57. Rotman, J.J., An Introduction to the Theory of Groups, 4th edn., Springer-Verlag, New York (1995).

    Book  MATH  Google Scholar 

  58. Schenkman, E., Group Theory, Van Nostrand, Princeton, NJ (1965).

    MATH  Google Scholar 

  59. Schmidt, O.J., Abstract Theory of Groups, 2nd edn., translated from the Russian by F. Holling and J.B. Roberts, Freeman, San Francisco (1966).

    Google Scholar 

  60. Scott, W.R., Group Theory, Prentice-Hall, Englewood Cliffs, NJ (1964).

    MATH  Google Scholar 

  61. Segal, D., Polycyclic Groups, Cambridge University Press, New York (1983).

    Book  MATH  Google Scholar 

  62. Serre, J.-P., Linear Representations of Finite Groups, translated from the French by L.L. Scott, Springer-Verlag, New York (1977).

    Chapter  Google Scholar 

  63. Specht, W., Gruppentheorie, Springer-Verlag, Berlin (1956).

    Book  MATH  Google Scholar 

  64. Speiser, A., Die Theorie der Gruppen von Endlicher Ordnung, 3rd edn., Springer-Verlag, Berlin (1937).

    MATH  Google Scholar 

  65. Steinberg, R., Lectures on Chevalley Groups, Yale University Press, New Haven (1967).

    Google Scholar 

  66. Suprunenko, D.A., Soluble and Nilpotent Linear Groups, Translation of Mathematics Monographs, American Mathematical Society (1963).

    Google Scholar 

  67. Suzuki, M., Structure of a Group and the Structure of Its Lattice of Subgroups, Springer-Verlag, Berlin (1956).

    Book  MATH  Google Scholar 

  68. Suzuki, M., Group Theory, Springer-Verlag, Berlin (1982).

    Google Scholar 

  69. Tomkinsori, M.J., FC-Groups, Pitman, Boston (1984).

    Google Scholar 

  70. Vaughan-Lee, M., The Restricted Burnside Problem, Oxford University Press, New York (1993).

    MATH  Google Scholar 

  71. Wehrfritz, B.A.F., Infinite Linear Groups, Springer-Verlag, Berlin (1973).

    Book  MATH  Google Scholar 

  72. Weinstein, M., Examples of Groups, Polygonal, Passaic, NJ (1977).

    MATH  Google Scholar 

  73. Weiss, E., Algebraic Number Theory, McGraw-Hill, New York (1963).

    MATH  Google Scholar 

  74. Wielandt, H., Finite Permutation Groups, translated from the German by R. Bercov, Academic Press, New York (1964).

    Google Scholar 

  75. Zassenhaus, H., The Theory of Groups, 2nd English edn., Chelsea, New York (1958).

    MATH  Google Scholar 

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    Derek J. S. Robinson

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Robinson, D.J.S. (1996). Infinite Soluble Groups. In: A Course in the Theory of Groups. Graduate Texts in Mathematics, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8594-1_15

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