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Lookup NU author(s): Dr John Britnell
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© 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.
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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