Degrees of rational characters of finite groups

Gabriel Navarro; Pham Huu Tiep

doi:10.1016/j.aim.2009.12.023

Degrees of rational characters of finite groups

Gabriel Navarro
, Pham Huu Tiep

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

29 Scopus citations

Abstract

A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result.

Original language	English (US)
Pages (from-to)	1121-1142
Number of pages	22
Journal	Advances in Mathematics
Volume	224
Issue number	3
DOIs	https://doi.org/10.1016/j.aim.2009.12.023
State	Published - Jun 2010
Externally published	Yes

Keywords

Normal p-complement
Rational character

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2009.12.023

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title = "Degrees of rational characters of finite groups",

abstract = "A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result.",

keywords = "Normal p-complement, Rational character",

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

note = "Funding Information: ✩ The research of the first author is partially supported by the Spanish Ministerio de Educaci{\'o}n y Ciencia proyecto MTM2007-61161, and a fellowship from Programa de Movilidad. The second author gratefully acknowledges the support of the NSF (grants DMS-0600967 and DMS-0901241). * Corresponding author. E-mail addresses: [email protected] (G. Navarro), [email protected] (P.H. Tiep).",

year = "2010",

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language = "English (US)",

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T1 - Degrees of rational characters of finite groups

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

N1 - Funding Information: ✩ The research of the first author is partially supported by the Spanish Ministerio de Educación y Ciencia proyecto MTM2007-61161, and a fellowship from Programa de Movilidad. The second author gratefully acknowledges the support of the NSF (grants DMS-0600967 and DMS-0901241). * Corresponding author. E-mail addresses: [email protected] (G. Navarro), [email protected] (P.H. Tiep).

PY - 2010/6

Y1 - 2010/6

N2 - A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result.

AB - A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result.

KW - Normal p-complement

KW - Rational character

UR - https://www.scopus.com/pages/publications/77952883947

UR - https://www.scopus.com/pages/publications/77952883947#tab=citedBy

U2 - 10.1016/j.aim.2009.12.023

DO - 10.1016/j.aim.2009.12.023

M3 - Article

AN - SCOPUS:77952883947

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VL - 224

SP - 1121

EP - 1142

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 3

ER -

Degrees of rational characters of finite groups

Abstract

Keywords

ASJC Scopus subject areas

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