Abelian Sylow subgroups in a finite group, II

Gabriel Navarro; Ronald Solomon; Pham Huu Tiep

doi:10.1016/j.jalgebra.2014.08.012

Abelian Sylow subgroups in a finite group, II

Gabriel Navarro, Ronald Solomon, Pham Huu Tiep

Mathematics

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

15 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 language	English (US)
Pages (from-to)	3-11
Number of pages	9
Journal	Journal of Algebra
Volume	421
DOIs	https://doi.org/10.1016/j.jalgebra.2014.08.012
State	Published - Jan 1 2015

Keywords

Abelian Sylow subgroups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2014.08.012

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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.",

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doi = "10.1016/j.jalgebra.2014.08.012",

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AU - Solomon, Ronald

AU - Tiep, Pham Huu

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N2 - 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.

AB - 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.

KW - Abelian Sylow subgroups

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Abelian Sylow subgroups in a finite group, II

Abstract

Keywords

ASJC Scopus subject areas

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