Abelian sylow subgroups in a finite group

Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticle

8 Citations (Scopus)

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

Fingerprint

Sylow Subgroup
Coprime
Finite Group
Subgroup
If and only if
Class

Keywords

  • Abelian Sylow subgroups
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Abelian sylow subgroups in a finite group. / Navarro, Gabriel; Tiep, Pham Huu.

In: Journal of Algebra, Vol. 398, 15.01.2014, p. 519-526.

Research output: Contribution to journalArticle

Navarro, Gabriel ; Tiep, Pham Huu. / Abelian sylow subgroups in a finite group. In: Journal of Algebra. 2014 ; Vol. 398. pp. 519-526.
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