On fixed-point-free automorphisms
Research output: Contribution to journal › Article › peer-review
Colleges, School and Institutes
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.
|Journal||Journal of Algebra|
|Early online date||12 Nov 2014|
|Publication status||Published - 1 Feb 2015|
- Automorphism, Fixed-point-free, Fitting height