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On finite groups admitting automorphisms with nilpotent fixed-point group

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 p′-group and A an elementary atelian group of operators on G. Suppose that A has order p3 and that if w ∈ A# then CG(w) is nilpotent. It is proved that G is nilpotent.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 2 , October 1971 , pp. 281 - 282
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston, London, 1968).Google Scholar
[2]Martineau, R.P., “On groups admitting a fixed point free automorphism group II”, (to appear).Google Scholar