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Groups with finiteness conditions and other restrictions for subgroups

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Literature cited

  1. H. Prüfer, “Unterschungen über die Zerlegbarkeit der abzähldaren primären Abelschen Gruppen,” Math. Z.,17, No. 1, 35–61 (1923).

    Google Scholar 

  2. A. G. Kurosh, “Zur Zerlegung unendlicher Gruppen,” Math. Ann.,106, No. 1, 107–113 (1932).

    Google Scholar 

  3. O. Yu. Shmidt, “Über unendliche Gruppen mit endlicher Kette,” Math. Z.,29, No. 1, 34–41 (1928).

    Google Scholar 

  4. A. I. Uzkov, “Über ein Theorem von Frobenius,” Mat. Sb.,1, No. 3, 337–339 (1936).

    Google Scholar 

  5. S. N. Chernikov, “Infinite special groups,” Mat. Sb.,6, No. 2, 199–214 (1939).

    Google Scholar 

  6. S. N. Chernikov, “Infinite, locally solvable groups,” Mat. Sb.,7, No. 1, 35–64 (1940).

    Google Scholar 

  7. S. N. Chernikov, “On the theory of infinite special groups,” Mat. Sb.,7, No. 3, 539–548 (1940).

    Google Scholar 

  8. S. N. Chernikov, “Finiteness conditions in the general theory of groups,” Usp. Mat. Nauk,14, No. 5, 45–96 (1959).

    Google Scholar 

  9. S. N. Chernikov, “Infinite groups with some prescribed properties of systems of infinite subgroups,” Dokl. Akad. Nauk SSSR,159, No. 4, 759–760 (1964).

    Google Scholar 

  10. S. N. Chernikov, “Groups with prescribed properties of systems of infinite subgroups,” Dokl. Akad. Nauk SSSR,171, No. 4, 806–809 (1966).

    Google Scholar 

  11. S. N. Chernikov, “Groups with prescribed properties of systems of infinite subgroups,” Ukr. Mat. Zh.,19, No. 6 111–121 (1967).

    Google Scholar 

  12. S. N. Chernikov, “Groups with systems of complemented subgroups,” Mat. Sb.,35, No. 2, 93–128 (1954).

    Google Scholar 

  13. A. G. Kurosh, Theory of Groups [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  14. O. Yu. Shmidt, “On infinite special groups,” Mat. Sb.,8, No. 3, 363–375 (1940).

    Google Scholar 

  15. A. I. Mal'tsev, “On an isomorphic representation of infinite groups by matrices,” Mat. Sb.,8, No. 3, 405–422 (1940).

    Google Scholar 

  16. N. N. Myagkova, “On groups of finite rank,” Izf. Akad. Nauk SSSR. Ser. Mat.,13, No. 6, 495–512 (1949).

    Google Scholar 

  17. D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups, 2 Vols., Springer, Berlin (1972).

    Google Scholar 

  18. V. P. Shunkov, “On the minimality problem for locally finite groups,” Algebra Logika,9, No. 2, 220–238 (1970).

    Google Scholar 

  19. O. H. Kegel and B. A. F. Wehrfritz, “Strong finiteness conditions in locally finite groups,” Math. Z.,117, No. 3, 309–324 (1970).

    Google Scholar 

  20. A. Yu. Ol'shanskii, “An infinite group with subgroups of prime orders,” Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 2, 309–321 (1980).

    Google Scholar 

  21. S. N. Chernikov, “On groups with a Sylow set,” Mat. Sb.,8, No. 3, 377–394 (1940).

    Google Scholar 

  22. A. G. Kurosh and S. N. Chernikov, “Solvable and nilpotent groups,” Usp. Mat. Nauk,2, No. 3, 18–59 (1947).

    Google Scholar 

  23. S. N. Chernikov, “On the theory of locally solvable groups,” Mat. Sb.,13, Vols. 2–3, 317–333 (1943).

    Google Scholar 

  24. A. I. Mal'tsev, “On a general method for obtaining local theorems of group theory,” Uch. Zap. Ivan. Pedagog. Inst.,1, 309 (1941).

    Google Scholar 

  25. H. Heineken and I. J. Mohamed, “A group with trivial center satisfying the normalizer condition,” J. Algebra,10, No. 3, 368–376 (1968).

    Google Scholar 

  26. Kourovka Notebook: Unsolved Problems of Group Theory [in Russian], 8-th ed., Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1982).

  27. S. N. Chernikov, “Complete groups having an ascending central series,” Mat. Sb.,18, No. 3, 397–422 (1946).

    Google Scholar 

  28. S. N. Chernikov, “On the theory of complete groups,” Mat. Sb.,22, No. 3, 319–348 (1948).

    Google Scholar 

  29. S. N. Chernikov, “On the centralizer of a complete Abelian normal subgroup of an infinite periodic group,” Dokl. Akad. Nauk SSSR,72, No. 2, 243–246 (1950).

    Google Scholar 

  30. S. N. Chernikov, “On periodic groups of automorphisms of extremal groups,” Mat. Zametki,4, No. 1, 91–96 (1968).

    Google Scholar 

  31. P. S. Novikov and S. I. Adyan, “On commutative subgroups and the conjugacy problem in free periodic groups of odd order,” Izv. Akad Nauk SSSR. Ser. Mat.,32, No. 5, 1176–1190 (1968).

    Google Scholar 

  32. S. N. Chernikov, “On special p-groups,” Mat. Sb.,27, No. 2, 185–200 (1950).

    Google Scholar 

  33. S. N. Chernikov, “On the theory of locally solvable groups with the minimality condition for subgroups,” Dokl. Akad. Nauk SSSR,65, No. 1, 21–24 (1949).

    Google Scholar 

  34. M. I. Kargapolov, “On a problem of O. Yu. Shmidt,” Sib. Mat. Zh.,4, No. 1, 232–235 (1963).

    Google Scholar 

  35. P. Hall and C. R. Kulatilaka, “A property of locally finite groups,” J. London Math. Soc.,39, No. 2, 235–239 (1964).

    Google Scholar 

  36. V. P. Shunkov, “On locally finite groups with the minimality condition for Abelian subgroups,” Algebra Logika,9, No. 5, 579–615 (1970).

    Google Scholar 

  37. M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  38. V. P. Shunkov, “On abstract characterizations of certain linear groups,” in: Algebra. Matrices and Matrix Groups [in Russian], Institute of Physics, Siberian Branch, Academy of Sciences of the USSR, Krasnoyarsk (1970), pp. 3–54.

    Google Scholar 

  39. V. S. Charin, “A remark on the minimality condition for subgroups,” Dokl. Akad. Nauk SSSR,66, No. 4, 575–576 (1949).

    Google Scholar 

  40. R. Baer, “Irreducible groups of automorphisms of Abelian groups,” Pac. J. Math.,14, No. 3, 385–406 (1964).

    Google Scholar 

  41. S. N. Chernikov, “Infinite layer-finite groups,” Mat. Sb.,22, No. 1, 101–133 (1948).

    Google Scholar 

  42. S. N. Chernikov, “On groups with finite conjugacy classes,” Dokl. Akad. Nauk SSSR,114, No. 6, 1177–1179 (1957).

    Google Scholar 

  43. S. N. Chernikov, “On layer-finite groups,” Mat. Sb.,45, No. 3, 415–416 (1958).

    Google Scholar 

  44. Yu. M. Gorchakov, Groups with Finite Conjugacy Classes [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  45. M. J. Tomkinson, FC-Groups, Pitman Advanced Publ. Program, Boston (1984).

    Google Scholar 

  46. S. N. Chernikov, “Infinite non-Abelian groups in which all infinite non-Abelian subgroups are invariant,” Ukr. Mat. Zh.,23, No. 5, 604–628 (1971).

    Google Scholar 

  47. P. Hall, “A characteristic property of soluble groups,” J. London Math. Soc.,12, No. 2, 198–200 (1937).

    Google Scholar 

  48. P. Hall, “Complemented groups,” J. London Math. Soc.,12, No. 2, 201–204 (1937).

    Google Scholar 

  49. N. V. Baeva, “Completely factorable groups,” Dokl. Akad. Nauk SSSR,92, No. 5, 877–880 (1953).

    Google Scholar 

  50. M. I. Kargapolov, “Some questions in the theory of solvable and nilpotent groups,” Dokl. Akad. Nauk SSSR,127, No. 6, 1164–1166 (1959).

    Google Scholar 

  51. Yu. M. Gorchakov, “Primitively factorable groups,” Uch. Zap. Perm. Univ.,17, 15–31 (1969).

    Google Scholar 

  52. S. N. Chernikov, Groups with Prescribed Properties of a System of Subgroups [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  53. S. N. Chernikov, “Finite supersolvable groups with Abelian Sylow subgroups,” in: Groups Determined by Properties of a System of Subgroups [in Russian], Institute of Mathematics, Academy of Sciences of the UKrSSR, Kiev (1979), pp. 3–15.

    Google Scholar 

  54. S. N. Chernikov, “Supersolvable groups with the minimality condition in which all primary subgroups are Abelian,” Algebra Logika,23, No. 6, 702–720 (1984).

    Google Scholar 

  55. S. N. Chernikov, “Locally supersolvable, periodic A-groups with the minimality condition for primary subgroups,” in: The Structure of Groups and Properties of Their Subgroups [in Russian], Institute of Mathematics, Academy of Sciences of the UkrSSR, Kiev (1968), pp. 5–21.

    Google Scholar 

  56. S. N. Chernikov, “Supersolvable, primarily elementary groups,” in: Studies of Groups with Prescribed Properties of Subgroups [in Russian], Institute of Mathematics, Academy of Sciences of the UkrSSR, Kiev (1981), pp. 3–13.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    V. S. Charin & D. I. Zaitsev

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  1. V. S. Charin
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  2. D. I. Zaitsev
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 3, pp. 277–287, May–June, 1988.

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Charin, V.S., Zaitsev, D.I. Groups with finiteness conditions and other restrictions for subgroups. Ukr Math J 40, 233–242 (1988). https://doi.org/10.1007/BF01061298

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