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On Burnside's lemma


Author: Marcel Herzog
Journal: Proc. Amer. Math. Soc. 28 (1971), 379-380
MSC: Primary 20.43
DOI: https://doi.org/10.1090/S0002-9939-1971-0274589-1
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)$.


References [Enhancements On Off] (What's this?)

  • [1] R. Brauer, On simple groups of order $ 5 \cdot {3^a} \cdot {2^b}$, Bull. Amer. Math. Soc. 74 (1968), 900-903. MR 38 #4552. MR 0236255 (38:4552)
  • [2] W. Feit, Characters of finite groups, Benjamin, New York, 1967. MR 36 #2715. MR 0219636 (36:2715)
  • [3] M. Herzog, On finite groups with cyclic Sylow subgroups for all odd primes, Israel J. Math. 6 (1968), 206-216. MR 38 #3349. MR 0235037 (38:3349)

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Additional Information

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

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