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Finite soluble groups admitting an automorphism of prime power order with few fixed points

Published online by Cambridge University Press:  24 October 2008

Brian Hartley  and
Volker Turau
Brian Hartley
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL
Volker Turau
Affiliation:
Institut für Informatik III, Universität Karlsruhe, 7500 Karlsruhe, West Germany
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Let G be a finite soluble group with Fitting subgroup F(G). The Fitting series of G is defined, as usual, by F0(G) = 1 and Fi(G)/Fi−1(G) = F(G/Fi−1(G)) for i ≥ 1, and the Fitting height h = h(G) of G is the least integer such that Fn(G) = G. Suppose now that a finite soluble group A acts on G. Let k be the composition length of A, that is, the number of prime divisors (counting multiplicities) of |A|. There is a certain amount of evidence in favour of the

CONJECTURE. |G:Fk(G)| is bounded by a number depending only on |A| and |CG(A)|.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 3 , November 1987 , pp. 431 - 441
Copyright
Copyright © Cambridge Philosophical Society 1987

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