Abelian Sylow subgroups in a finite group, II

Gabriel Navarro, Ronald Solomon, Pham Huu Tiep

Research output: Contribution to journalArticle

3 Citations (Scopus)

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
StatePublished - Jan 1 2015

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Sylow Subgroup
Coprime
Finite Group
Irreducible Character
Subgroup
If and only if
Class

Keywords

  • Abelian Sylow subgroups

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Abelian Sylow subgroups in a finite group, II. / Navarro, Gabriel; Solomon, Ronald; Tiep, Pham Huu.

In: Journal of Algebra, Vol. 421, 01.01.2015, p. 3-11.

Research output: Contribution to journalArticle

Navarro, Gabriel ; Solomon, Ronald ; Tiep, Pham Huu. / Abelian Sylow subgroups in a finite group, II. In: Journal of Algebra. 2015 ; Vol. 421. pp. 3-11.
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