Abelian Sylow subgroups in a finite group, II

Gabriel Navarro, Ronald Solomon, Pham Huu Tiep

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let p 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, and, if p∈. {3, 5}, the degree of every irreducible character in the principal p-block of G is coprime to p. This gives a complete solution to a problem posed by R. Brauer in 1963.

Original languageEnglish (US)
Pages (from-to)3-11
Number of pages9
JournalJournal of Algebra
Volume421
DOIs
Publication statusPublished - Jan 1 2015

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Keywords

  • Abelian Sylow subgroups

ASJC Scopus subject areas

  • Algebra and Number Theory

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