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Group Theory pp 130–142Cite as

Locally soluble groups satisfying the minimal condition for normal subgroups

Part of the Lecture Notes in Mathematics book series (LNM,volume 573)

Keywords

  • Normal Subgroup
  • Minimal Condition
  • Nilpotent Group
  • Finite Index
  • Minimal Normal Subgroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  • Reinhold Baer (1949), "Groups with descending chain condition for normal subgroups", Duke Math. J. 16, 1–22. MR10,506.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Reinhold Baer (1957), "Lokal Noethersche Gruppen", Math. Z. 66 (1956/57), 341–363. MR19,12.

    MathSciNet  MATH  Google Scholar 

  • Reinhold Baer (1964), "Irreducible groups of automorphisms of abelian groups", Pacific J. Math. 14, 385–406. MR29#2310.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • В.С. Чарин [V.S. Čarin] (1949), "Замечанив об условии минимальности для подгрупп" [A remark on the minimal condition for subgroups], Dokl. Akad. Nauk SSSR (N.S.) 66, 575–576. MR10,677.

    Google Scholar 

  • В.С. Чарин [V.S. Čarin] (1953), "Об условии минимальности для нормальных селителей локально раэрешимых групп" [On the minimal condition for normal divisors of a locally soluble group], Mat. Sb. (N.S.) 33 (75), 27–36. MR15,197.

    Google Scholar 

  • С.Н. Черников [S.N. Černikov] (1940), "Бесконечные локально разрешимые группы" [Infinite locally soluble groups], Rec. Math. [Mat. Sb.] (N.S.) 7 (49), 35–64.

    Google Scholar 

  • С.Н. Черников [S.N. Černikov] (1949), "К теории локально разрешимых групп с условием минимальности для подгрупп" [On the theory of locally soluble groups with the minimal condition for subgroups], Dokl. Akad. Nauk SSSR (N.S.) 65, 21–24, MR10,590.

    Google Scholar 

  • Charles W. Curtis, Irving Reiner (1962), Representation Theory of Finite Groups and Associative Algebras (Pure and Applied Mathematics, 11. Interscience [John Wiley & Sons], New York, London). MR26#2519.

    MATH  Google Scholar 

  • A.D. Gardiner and B. Hartley and M.J. Tomkinson (1971), "Saturated formations and Sylow structure in locally finite groups", J. Algebra 17, 177–211. MR42#7778.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • P. Hall (1954), "Finiteness conditions for soluble groups", Proc. London Math. Soc. (3) 4, 419–436. MR17,344.

    MathSciNet  MATH  Google Scholar 

  • B. Hartley (1971), "Sylow subgroups of locally finite groups", Proc. London Math. Soc. (3) 23, 159–192. MR46#3623.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • B. Hartley and D. McDougall (1971), "Injective modules and soluble groups satisfying the minimal condition for normal subgroups", Bull. Austral. Math. Soc. 4, 113–135. MR43#2067.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • H. Heineken and J.S. Wilson (1974), "Locally soluble groups with MIN-n", J. Austral. Math. Soc. 17, 305–318. MR50#7351.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C.H. Houghton, J.C. Lennox and James Wiegold (1975), "Centrality in wreath products", J. Algebra 35, 356–366.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • L.G. Kovács and M.F. Newman (1962), "Direct complementation in groups with operators", Arch. der Math. 13, 427–433. MR26#5079.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • J.C. Lennox and J.E. Roseblade (1970), "Centrality in finitely generated soluble groups", J. Algebra 16, 399–435. MR42#4633.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • David McDougall (1970), "Soluble groups with the minimum condition for normal subgroups", Math. Z. 118, 157–167. MR46#7385.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • D.H. McLain (1959), "Finiteness conditions in locally soluble groups", J. London Math. Soc. 34, 101–107. MR21#2003.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Ю.М. Межебовский [Ju.M. Mežebovskiĭ] (1972), "О группах, обладающих возраст ающим инвариантным рядом с конечными факторами" [On groups having an ascending invariant series with finite factors], Sibirsk. Mat. Ž. 13, 473–476; Siberian Math. J. 13 (1972), 328-330. MR45#8738.

    MathSciNet  Google Scholar 

  • М.М. Мурач [M.M. Murač] (1973), "Про FC-розв'язнi групи автоморфiзмiв розв'язних груп скiнченного рангу" [FC-solvable groups of automorphisms of solvable groups of finite rank], Dopovīdī Akad. Nauk Ukrain. RSR Ser. A 1973, 696–698; 764. MR48#4126.

    Google Scholar 

  • Derek J.S. Robinson (1972), Finiteness Conditions and Generalized Soluble Groups, Part 1 (Ergebnisse der Mathematik und ihrer Grenzgebiete, 62. Springer-Verlag, Berlin, Heidelberg, New York). MR48#11314.

    CrossRef  MATH  Google Scholar 

  • J.E. Roseblade and J.S. Wilson (1971), "A remark about monolithic groups", J. London Math. Soc. (2) 3, 361–362. MR43#7502.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Howard L. Silcock (1974), "Metanilpotent groups satisfying the minimal condition for normal subgroups", Math. Z. 135, 165–173. MR51#711.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Howard L. Silcock (1975), "On the construction of soluble groups satisfying the minimal condition for normal subgroups", Bull. Austral. Math. Soc. 12, 231–257. ZblM292#20027.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • P.W. Stroud (1966), "Topics in the theory of verbal subgroups", Doctoral Dissertation, Cambridge, 1966.

    Google Scholar 

  • John S. Wilson (1970), "Some properties of groups inherited by normal subgroups of finite index", Math. Z. 114, 19–21. MR41#3577.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • John S. Wilson (1974), "A note on subsoluble groups", Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973, 717–718 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York, 1974). ZblM292#20029.

    Google Scholar 

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Wilson, J.S. (1977). Locally soluble groups satisfying the minimal condition for normal subgroups. In: Bryce, R.A., Cossey, J., Newman, M.F. (eds) Group Theory. Lecture Notes in Mathematics, vol 573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087819

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  • DOI: https://doi.org/10.1007/BFb0087819

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