Hostname: page-component-f554764f5-246sw Total loading time: 0 Render date: 2025-04-10T17:54:46.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphism towers of certain almost soluble groups

Published online by Cambridge University Press:  24 October 2008

J. A. Hulse
J. A. Hulse
Affiliation:
Mathematical Institute, University of Edinburgh, Scotland
Get access Rights & Permissions [Opens in a new window]

Extract

Automorphism towers were first considered in (19) with the case of finite groups. Recently polycyclic and extremal groups were considered in (7) and (12) respectively. The purpose of this paper is to consider automorphism towers of groups in a class of almost soluble groups which contains all polycyclic and all extremal groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 397 - 420
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Baer, R.Finite extensions of Abelian groups with minimum condition. Trans. Amer. Math. Soc. 79 (1955), 521–540.CrossRefGoogle Scholar
(2)Černikov, S. N.Finiteness conditions in the general theory of groups. Amer. Math. Soc. Transl. (2) 84 (1969), 1–67. (Translation from Uspehi. Mat. Nauk 14 (1959), 45–96.)Google Scholar
(3)Fuchs, L.Abelian groups 3rd ed. (Oxford, Pergamon Press, 1960).Google Scholar
(4)Hall, P.Nilpotent groups (Canadian Mathematical Congress, Alberta, 1957, republished as Queen Mary College Mathematics Notes, London, 1969).Google Scholar
(5)Hall, P.Some sufficient conditions for a group to be nilpotent. Illinois J. Math. 2 (1958), 787–801.CrossRefGoogle Scholar
(6)Hall, P. and Hartley, B.The stability group of a series of subgroups. Proc. London Math. Soc. (3) 16 (1966), 1–39.Google Scholar
(7)Hulse, J. A.Automorphism towers of polycyclic groups. J. Algebra 16 (1970), 347–398.CrossRefGoogle Scholar
(8)Hulse, J. A.Joins of ascendant subgroups. Proc. London Math. Soc. 25 (3) (1972), 399–412.Google Scholar
(9)Kegel, O. H.Über den Normalisator von subnormalen und erreichbaren Untergruppen. Math. Ann. 163 (1966), 248–258.CrossRefGoogle Scholar
(10)MalČev, A. I.On certain classes of infinite soluble groups. Amer. Math. Soc. Transl. (2) 2 (1956), 1–21. (Translation from Mat. Sb. (N.S.) 28 (70) (1951), 567–588.)Google Scholar
(11)Plotkin, B. I.Groups of automorphism8 of algebraic systems (Groningen, Wolters-Noordhoff, 1972).Google Scholar
(12)Rae, A. and Roseblade, J. E.Automorphism towers of extremal groups. Math. Z. 117 (1970), 70–75.CrossRefGoogle Scholar
(13)Robinson, D. J. S.Infinite soluble and nilpotent groups (QueenMary College Mathematics Notes, London, 1967).Google Scholar
(14)Robinson, D. J. S.On soluble minimax groups. Math. Z. 101 (1967), 13–40.CrossRefGoogle Scholar
(15)Robinson, D. J. S.Finiteness conditions on subnormal and ascendant Abelian subgroups. J. Algebra 10 (1968), 333–359.Google Scholar
(16)Robinson, D. J. S.Residual properties of some classes of infinite soluble groups. Proc. London Math. Soc. (3) 18 (1968), 495–520.Google Scholar
(17)Robinson, D. J. S.Finiteness conditions and generalized soluble groups, parts 1 and 2 (Berlin, Springer-Verlag, 1972).Google Scholar
(18)Wehrfritz, B. A. F.Groups of automorphisms of soluble groups. Proc. London Math. Soc. (3) 20 (1970), 101–122.CrossRefGoogle Scholar
(19)Wielandt, H.Eine Verallgemeinerung der invarianten Untergruppen. Math. Z. 45 (1939), 209–244.CrossRefGoogle Scholar