On fixed-point-free automorphisms

Glen Collins, Paul Flavell

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
208 Downloads (Pure)

Abstract

Let R be a cyclic group of prime order which acts on the extraspecial group F in such a way that F=[F,R]. Suppose RF acts on a group G so that CG(F)=1 and (|R|,|G|)=1. It is proved that F(CG(R))⊆F(G). As corollaries to this, it is shown that the Fitting series of CG(R) coincides with the intersections of CG(R) with the Fitting series of G , and that when |R| is not a Fermat prime, the Fitting heights of CG(R) and G are equal.
Original languageEnglish
Pages (from-to)798-811
JournalJournal of Algebra
Volume423
Early online date12 Nov 2014
DOIs
Publication statusPublished - 1 Feb 2015

Keywords

  • Automorphism
  • Fixed-point-free
  • Fitting height

Fingerprint

Dive into the research topics of 'On fixed-point-free automorphisms'. Together they form a unique fingerprint.

Cite this