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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On Burnside's lemma


Author: Marcel Herzog
Journal: Proc. Amer. Math. Soc. 28 (1971), 379-380
MSC: Primary 20.43
MathSciNet review: 0274589
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Abstract: Burnside's lemma on characters of finite groups is generalized, leading to the following theorem: if $ G$ is a simple group of order divisible by exactly 3 primes, and if one of the Sylow subgroups of $ G$ is cyclic, then for each Sylow subgroup $ P$ of $ G$ we have $ {C_G}(P) = Z(P)$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0274589-1
Keywords: Finite group, ordinary irreducible character, simple group, conjugate class
Article copyright: © Copyright 1971 American Mathematical Society