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Automorphisms fixing every subnormal subgroup of a finite group

Published online by Cambridge University Press:  18 May 2009

John Cossey
John Cossey
Affiliation:
Mathematics Department, School of Mathematical Sciences, Australian National University, Canberra 0200, Australia
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We denote by Autsn(G) the set of all automorphisms that fix every subnormal subgroup of G setwise. In a recent paper [7] Robinson showed that the structure of Autsn(G) is quite restricted for a finite group G. Our aim in this paper is to show that more detailed information about the structure of Autsn(G) can be obtained by focussing on its action on F*(G), the generalised Fitting subgroup of G.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 1 , January 1997 , pp. 111 - 114
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Aschbacher, M., Finite group theory, Cambridge studies in advanced mathematics 10 (Cambridge, 1986).Google Scholar
2.Cooper, C. D. H., Power automorphisms of a group, Math. Z. 107 (1968), 335–356.CrossRefGoogle Scholar
3.Molle, Marianna Dalle, Sugli automorphismi che fissano i sottogruppi subnormalidi un gruppo risolubile, Bol. Un. Mat. Ital., A(7) 9 (1995), 483–491.Google Scholar
4.Franciosi, Silvana and Giovanni, Francesco de, On automorphisms fixing subnormal subgroups of soluble groups, Atti Accad. Rend. fis. 8 (1988), 217–222.Google Scholar
5.Hall, Philip, Some sufficient conditions for a group to be nilpotent, Illinois J. Math. 2 (1957), 787–801.Google Scholar
6.Huppert, B. and Blackburn, N., Finite groups III (Springer-Verlag, 1982).CrossRefGoogle Scholar
7.Robinson, Derek J. S., Automorphisms fixing every subnormal subgroup of a finite group, Arch. Math. (Basel) 64 (1995), 1–4.CrossRefGoogle Scholar