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On exceptional groups of order p⁵

On exceptional groups of order p⁵

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 / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 13 Jun 2018 15:10
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: GREAT b
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/20066

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