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arXiv · 1408.1649

On exceptional groups of order p^5

John R. Britnell·Neil Saunders·Tony Skyner
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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 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.

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John R. Britnell, Neil Saunders, Tony Skyner. 2014-08-07. On exceptional groups of order p^5. https://arxiv.org/abs/1408.1649

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