Finite groups and Lie rings with an automorphism of order $2^n$

Khukhro, E. I. and Makarenko, N. Yu. and Shumyatsky, P. (2015) Finite groups and Lie rings with an automorphism of order $2^n$. [MIMS Preprint]

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Abstract

Suppose that a finite group $G$ admits an automorphism $\f$ of order $2^n$ such that the fixed-point subgroup $C_G(\f ^{2^{n-1}})$ of the involution $\f ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\f )|$ be the number of fixed points of $\f$. It is proved that $G$ has a soluble subgroup of derived length bounded in terms of $n,c$ whose index is bounded in terms of $m,n,c$. A similar result is also proved for Lie rings.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Professor Evgeny Khukhro
Date Deposited:	24 Feb 2015
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2257

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