On burnside’s lemma

Marcel Herzog*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 CG(P) =Z(P).

Original languageEnglish
Pages (from-to)379-380
Number of pages2
JournalProceedings of the American Mathematical Society
Volume28
Issue number2
DOIs
StatePublished - May 1971

Keywords

  • Conjugate class
  • Finite group
  • Ordinary irreducible character
  • Simple group

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