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Irreducible Automorphisms of Certain p-Groups

Published online by Cambridge University Press:  20 November 2018

D. Ž. Djoković  and
J. Malzan
D. Ž. Djoković
Affiliation:
University of Waterloo, Waterloo, Ontario
J. Malzan
Affiliation:
University of Waterloo, Waterloo, Ontario
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Abstract

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The chief purpose of this paper is to find all pairs (G, θ) where G is a finite special p-group, and θ is an automorphism of G acting trivially on the Frattini subgroup and irreducibly on the Frattini quotient. This problem arises in the context of describing finite groups having an abelian maximal subgroup. In fact, we solve a more general problem for a wider class of p-groups, which we call special F-groups, where F is a finite field of characteristic p. We point out that if p is odd, then an F-group has exponent p. On the other hand, every special 2-group is also a special GF(2)-group.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 333 - 348
Copyright
Copyright © Canadian Mathematical Society 1977

References

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