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On finite soluble groups and the fixed-point groups of automorphisms

Published online by Cambridge University Press:  17 April 2009

J.N. Ward
J.N. Ward
Affiliation:
University of Sydney, Sydney, New South Wales.
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Abstract

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Let p denote a prime, G a. finite soluble p'-group and A an elementary abelian p-group of operators on G. Suppose that A has order p4 and that if ω ∈ A# then CG(ω) has nilpotent derived group. Then G has nilpotent derived group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 375 - 378
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston, London, 1968).Google Scholar
[2]Kovács, L.G. and Wall, G.E., “Involutory automorphisms of groups of odd order and their fixed point groups”, Nagoya Math. J. 27 (1966), 113–120.Google Scholar
[3]Ward, J.N., “Automorphisms of finite groups and their fixed-point groups”, J. Austral. Math. Soc. 9 (1969), 467–477.Google Scholar