Abelian sylow subgroups in a finite group

Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Let p ≠ 3, 5 be a prime. We prove that Sylow p-subgroups of a finite group G are abelian if and only if the class sizes of the p-elements of G are all coprime to p. This gives a solution to a problem posed by R. Brauer in 1956 (for p ≠ 3, 5).

Original languageEnglish (US)
Pages (from-to)519-526
Number of pages8
JournalJournal of Algebra
Volume398
DOIs
StatePublished - Jan 15 2014

Keywords

  • Abelian Sylow subgroups
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Algebra and Number Theory

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