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Elementary abelian operator groups and admissible formations

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Fletcher Gross
Fletcher Gross
Affiliation:
Department of Pure Mathematics Australian National UniversityCanberra ACT 2600, Australia Department of Mathematics University of UtahSalt Lake City Utah 84112, U.S.A.
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Abstract

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Suppose the elementary abelian group A acts on the group G where A and G have relatively prime orders. If CG(a) belongs to some formation F for all non-identity elements a in A, does it follow that G belongs to F? For many formations, the answer is shown to be yes provided that the rank of A is sufficiently large.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 1 , February 1983 , pp. 71 - 91
Copyright
Copyright © Australian Mathematical Society 1983

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