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 |
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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: | http://eprints.maths.manchester.ac.uk/id/eprint/2257 |

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