A note on groups in which the centraliser of every element of order 5 is a 5-group
Group Theory
2012-04-04 v2
Abstract
The main theorem in this article shows that a group of odd order which admits the alternating group of degree 5 with an element of order 5 acting fixed point freely is nilpotent of class at most two. For all odd primes r, other than 5, we give a class two r-group which admits the alternating group of degree 5 in such a way. This theorem corrects an earlier result which asserts that such class two groups do not exist. The result allows us to state a theorem giving precise information about groups in which the centralizer of every element of order 5 has centralizer a 5-group.
Cite
@article{arxiv.1103.3581,
title = {A note on groups in which the centraliser of every element of order 5 is a 5-group},
author = {Sarah Astill and Chris Parker and Rebecca Waldecker},
journal= {arXiv preprint arXiv:1103.3581},
year = {2012}
}