Britnell, John R., Saunders, Neil and Skyner, Tony (2016) On exceptional groups of order p⁵. Journal of Pure and Applied Algebra, 221 (11). pp. 2647-2665. ISSN 0022-4049 (doi:https://doi.org/10.1016/j.jpaa.2016.12.009)

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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 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.

Item Type:	Article
Uncontrolled Keywords:	Finite Groups, Symmetric Groups, p-Groups
Subjects:	Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS) Faculty of Engineering & Science
Last Modified:	04 Mar 2022 13:07
URI:	http://gala.gre.ac.uk/id/eprint/20066

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