Recognizing Abelian Sylow Subgroups in Finite Groups |
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Authors: | Julian Brough |
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Institution: | 1. Faculty of Mathematics , Centre for Mathematical Sciences , Cambridge, England , UK jmab6@cam.ac.uk |
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Abstract: | Let p be a prime. We prove that if a finite group G has non-abelian Sylow p-subgroups, and the class size of every p-element in G is coprime to p, then G contains a simple group as a subquotient which exhibits the same property. In addition, we provide a list of all the simple groups and primes such that the Sylow p-subgroups are non-abelian and all p-elements have class size coprime to p. |
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Keywords: | Abelian Sylow subgroups |
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