P-Parts of Brauer character degrees

Gabriel Navarro; Pham Huu Tiep; Hung P. Tong-Viet

doi:10.1016/j.jalgebra.2014.01.022

P-Parts of Brauer character degrees

Gabriel Navarro, Pham Huu Tiep, Hung P. Tong-Viet

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

1 Scopus citations

Abstract

Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.

Original language	English (US)
Pages (from-to)	426-438
Number of pages	13
Journal	Journal of Algebra
Volume	403
DOIs	https://doi.org/10.1016/j.jalgebra.2014.01.022
State	Published - Feb 1 2014
Externally published	Yes

Keywords

Brauer characters
Solvable groups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2014.01.022

Cite this

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title = "P-Parts of Brauer character degrees",

abstract = "Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.",

keywords = "Brauer characters, Solvable groups",

author = "Gabriel Navarro and Tiep, {Pham Huu} and Tong-Viet, {Hung P.}",

note = "Funding Information: 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 ). The research of the third author is supported by a Startup Research Fund from the College of Agriculture, Engineering and Science, the University of KwaZulu-Natal. ",

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doi = "10.1016/j.jalgebra.2014.01.022",

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AU - Navarro, Gabriel

AU - Tiep, Pham Huu

AU - Tong-Viet, Hung P.

N1 - Funding Information: 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 ). The research of the third author is supported by a Startup Research Fund from the College of Agriculture, Engineering and Science, the University of KwaZulu-Natal.

PY - 2014/2/1

Y1 - 2014/2/1

N2 - Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.

AB - Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.

KW - Brauer characters

KW - Solvable groups

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DO - 10.1016/j.jalgebra.2014.01.022

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VL - 403

SP - 426

EP - 438

JO - Journal of Algebra

JF - Journal of Algebra

ER -

P-Parts of Brauer character degrees

Abstract

Keywords

ASJC Scopus subject areas

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