Abelian sylow subgroups in a finite group

Gabriel Navarro; Pham Huu Tiep

doi:10.1016/j.jalgebra.2013.04.007

Abelian sylow subgroups in a finite group

Gabriel Navarro
, Pham Huu Tiep

Research output: Contribution to journal › Article › peer-review

24 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 language	English (US)
Pages (from-to)	519-526
Number of pages	8
Journal	Journal of Algebra
Volume	398
DOIs	https://doi.org/10.1016/j.jalgebra.2013.04.007
State	Published - Jan 15 2014
Externally published	Yes

Keywords

Abelian Sylow subgroups
Primary
Secondary

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2013.04.007

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title = "Abelian sylow subgroups in a finite group",

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).",

keywords = "Abelian Sylow subgroups, Primary, Secondary",

author = "Gabriel Navarro and Tiep, \{Pham Huu\}",

note = "Funding Information: ✩ The authors are grateful to the referee for helpful comments on the paper. ✩✩ The research of the first author is supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296. The second author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374). * Corresponding author. E-mail addresses: [email protected] (G. Navarro), [email protected] (P.H. Tiep).",

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doi = "10.1016/j.jalgebra.2013.04.007",

language = "English (US)",

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journal = "Journal of Algebra",

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T1 - Abelian sylow subgroups in a finite group

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

N1 - Funding Information: ✩ The authors are grateful to the referee for helpful comments on the paper. ✩✩ The research of the first author is supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296. The second author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374). * Corresponding author. E-mail addresses: [email protected] (G. Navarro), [email protected] (P.H. Tiep).

PY - 2014/1/15

Y1 - 2014/1/15

N2 - 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).

AB - 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).

KW - Abelian Sylow subgroups

KW - Primary

KW - Secondary

UR - https://www.scopus.com/pages/publications/84887149568

UR - https://www.scopus.com/pages/publications/84887149568#tab=citedBy

U2 - 10.1016/j.jalgebra.2013.04.007

DO - 10.1016/j.jalgebra.2013.04.007

M3 - Article

AN - SCOPUS:84887149568

SN - 0021-8693

VL - 398

SP - 519

EP - 526

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Abelian sylow subgroups in a finite group

Abstract

Keywords

ASJC Scopus subject areas

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