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On exceptional groups of order p5

Lookup NU author(s): Dr John Britnell

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Abstract

© 2016A 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 p5. For an odd prime p, we classify all pairs (G,Q) where G has order p5 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 p5 with at least one exceptional quotient tends to 1/2.

Publication metadata

Author(s): Britnell JR, Saunders N, Skyner T

Publication type: Article

Publication status: Published

Journal: Journal of Pure and Applied Algebra

Year: 2017

Volume: 221

Issue: 11

Pages: 2647-2665

Print publication date: 01/11/2017

Online publication date: 27/12/2016

Acceptance date: 31/10/2016

ISSN (print): 0022-4049

ISSN (electronic): 1873-1376

Publisher: Elsevier B.V.

URL: https://doi.org/10.1016/j.jpaa.2016.12.009

DOI: 10.1016/j.jpaa.2016.12.009

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