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Involutory Automorphisms of Groups of odd Order and Their Fixed Point Groups

Published online by Cambridge University Press:  22 January 2016

L. G. Kovács  and
G. E. Wall
L. G. Kovács
Affiliation:
Australian National University and University of Sydney
G. E. Wall
Affiliation:
Australian National University and University of Sydney
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Let G be a finite group of odd order with an automorphism θ of order 2. (We use without further reference the fact, established by W. Feit and J. G. Thompson, that all groups of odd order are soluble.) Let Gθ denote the subgroup of G formed by the elements fixed under θ. It is an elementary result that if Gθ = 1 then G is abelian. But if we merely postulate that Gθ be cyclic, the structure of G may be considerably more complicated—indeed G may have arbitrarily large soluble length.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 113 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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