On exceptional groups of order p5 |
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Authors: | John R Britnell Neil Saunders Tony Skyner |
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Institution: | 1. Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom;2. Department of Mathematics, City University London, Northampton Square, London EC1V 0HB, United Kingdom;3. Heilbronn Institute for Mathematical Research, University of Bristol, School of Mathematics, University Walk, Bristol BS8 1TW, United Kingdom |
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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 . For an odd prime p, we classify all pairs where G has order and Q is a distinguished quotient. (The case has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order with at least one exceptional quotient tends to 1/2. |
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Keywords: | Primary 20B35 secondary 20D15 |
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