On exceptional groups of order p^5
Group Theory
2014-08-08 v1
Abstract
A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient. The smallest examples of exceptional p-groups have order p^5. For an odd prime p, we classify all pairs (G,Q) where G has order p^5 and Q is a distinguished quotient. (The case p=2 has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order p^5 with at least one exceptional quotient tends to 1/2.
Cite
@article{arxiv.1408.1649,
title = {On exceptional groups of order p^5},
author = {John R. Britnell and Neil Saunders and Tony Skyner},
journal= {arXiv preprint arXiv:1408.1649},
year = {2014}
}
Comments
23 pages