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On supersolubility in some groups with finitely generated Fitting radical


Authors: James C. Beidleman and Howard Smith
Journal: Proc. Amer. Math. Soc. 114 (1992), 319-324
MSC: Primary 20F16
DOI: https://doi.org/10.1090/S0002-9939-1992-1069288-6
MathSciNet review: 1069288
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Abstract: The groups $ G$ considered in this paper have the property that every normal nonsupersoluble subgroup of $ G$ has a finite, $ G$-invariant, nonsupersoluble image. The structure of a certain radical, defined in terms of ascendant supersoluble subgroups, is determined. The main result is a supersolubility criterion for polycyclic groups.


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  • [1] R. Baer, Nilgruppen, Math. Z. 62 (1955), 402-437. MR 0071424 (17:124e)
  • [2] -, Classes of finite groups and their properties, Illinois J. Math. 1 (1957), 115-187. MR 0087655 (19:386d)
  • [3] -, Überauflösbare Gruppen, Abh. Math. Sem. Univ. Hamburg 23 (1957), 11-28.
  • [4] J. C. Beidleman and D. J. S. Robinson, On the structure of the normal subgroups of a group: Supersolubility, Rend. Sem. Mat. Univ. Padova (to appear). MR 1183906 (93i:20040)
  • [5] K. W. Gruenberg, The Engel elements of a soluble group, Illinois J. Math. 3 (1959), 151-168. MR 0104730 (21:3483)
  • [6] P. Hall, On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595-622. MR 0110750 (22:1618)
  • [7] -, The Frattini subgroups of finitely generated groups, Proc. London Math. Soc. (3) 11 (1961), 327-352. MR 0124406 (23:A1718)
  • [8] B. Huppert, Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z. 60 (1954), 409-434. MR 0064771 (16:332a)
  • [9] O. U. Kramer, Über Durchschnitte von Untergruppen endlicher auflösbarer Gruppen, Math. Z. 148 (1976), 89-97. MR 0407135 (53:10918)
  • [10] J. C. Lennox, A supersolubility criterion for finitely generated hyper-(abelian-by-finite) groups, Arch. Math. 24 (1973), 247-248. MR 0318318 (47:6865)
  • [11] A. I. Mal'cev, On certain classes of infinite soluble groups, Amer. Math. Soc. Transl. 2 (1956), 1-21. MR 0075950 (17:824d)
  • [12] D. J. S. Robinson, Finiteness conditions and generalised soluble groups, vol. 1, Springer-Verlag, Berlin, 1972.
  • [13] -, A course in the theory of groups, Springer-Verlag, New York, 1982. MR 648604 (84k:20001)
  • [14] W. R. Scott, Group theory, Prentice-Hall, New Jersey, 1964. MR 0167513 (29:4785)
  • [15] B. A. F. Wehrfritz, Infinite linear groups, Springer-Verlag, Berlin, 1973. MR 0335656 (49:436)
  • [16] M. Weinstein, Between nilpotent and solvable, Polygonal Publ. House, 1982. MR 655785 (84k:20002)
  • [17] H. Wielandt, Eine Verallgemeinerung der invarianten Untergruppen, Math. Z. 45 (1939), 209-244. MR 1545814

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DOI: https://doi.org/10.1090/S0002-9939-1992-1069288-6
Article copyright: © Copyright 1992 American Mathematical Society

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