# On finite soluble groups with almost fixed-point-free automorphisms of non-coprime order

Khukhro, E. I. (2016) On finite soluble groups with almost fixed-point-free automorphisms of non-coprime order. [MIMS Preprint]

## Abstract

It is proved that if a finite $p$-soluble group $G$ admits an automorphism $\varphi$ of order $p^n$ having at most $m$ fixed points on every $\f$-invariant elementary abelian $p'$-section of $G$, then the $p$-length of $G$ is bounded above in terms of $p^n$ and $m$; if in addition the group $G$ is soluble, then the Fitting height of $G$ is bounded above in terms of $p^n$ and $m$. It is also proved that if a finite soluble group $G$ admits an automorphism $\psi$ of order $p^aq^b$ for some primes $p,q$, then the Fitting height of $G$ is bounded above in terms of $|\psi |$ and $|C_G(\psi )|$.

Item Type: MIMS Preprint MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations Professor Evgeny Khukhro 08 Mar 2016 08 Nov 2017 18:18 http://eprints.maths.manchester.ac.uk/id/eprint/2448