Degrees and p-rational characters

Gabriel Navarro; Pham Huu Tiep

doi:10.1112/blms/bds054

Degrees and p-rational characters

Gabriel Navarro, Pham Huu Tiep

Mathematics

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

6 Scopus citations

Abstract

Suppose that G is a finite group and that p is a prime number. We prove that if every p-rational irreducible character of G is non-zero on every p-element of G, then G has a normal Sylow p-subgroup. This yields a p-rational refinement of the Itô-Michler theorem: if p does not divide the degree of any irreducible p-rational character of G, then G has a normal Sylow p-subgroup

Original language	English (US)
Pages (from-to)	1246-1250
Number of pages	5
Journal	Bulletin of the London Mathematical Society
Volume	44
Issue number	6
DOIs	https://doi.org/10.1112/blms/bds054
State	Published - Dec 2012

ASJC Scopus subject areas

General Mathematics

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title = "Degrees and p-rational characters",

abstract = "Suppose that G is a finite group and that p is a prime number. We prove that if every p-rational irreducible character of G is non-zero on every p-element of G, then G has a normal Sylow p-subgroup. This yields a p-rational refinement of the It{\^o}-Michler theorem: if p does not divide the degree of any irreducible p-rational character of G, then G has a normal Sylow p-subgroup",

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

note = "Funding Information: The research of the first author was partially supported by the Spanish Ministerio de Educaci{\'o}n y Ciencia MTM2010-15296, and Prometeo/Generalitat Valenciana. The second author gratefully acknowledges the support of the NSF (grant DMS-0901241).",

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AU - Navarro, Gabriel

AU - Tiep, Pham Huu

N1 - Funding Information: The research of the first author was partially supported by the Spanish Ministerio de Educación y Ciencia MTM2010-15296, and Prometeo/Generalitat Valenciana. The second author gratefully acknowledges the support of the NSF (grant DMS-0901241).

PY - 2012/12

Y1 - 2012/12

N2 - Suppose that G is a finite group and that p is a prime number. We prove that if every p-rational irreducible character of G is non-zero on every p-element of G, then G has a normal Sylow p-subgroup. This yields a p-rational refinement of the Itô-Michler theorem: if p does not divide the degree of any irreducible p-rational character of G, then G has a normal Sylow p-subgroup

AB - Suppose that G is a finite group and that p is a prime number. We prove that if every p-rational irreducible character of G is non-zero on every p-element of G, then G has a normal Sylow p-subgroup. This yields a p-rational refinement of the Itô-Michler theorem: if p does not divide the degree of any irreducible p-rational character of G, then G has a normal Sylow p-subgroup

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ER -

Degrees and p-rational characters

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