Mckay natural correspondences on characters

Gabriel Navarro; Pham Huu Tiep; Carolina Vallejo

doi:10.2140/ant.2014.8.1839

Mckay natural correspondences on characters

Gabriel Navarro, Pham Huu Tiep, Carolina Vallejo

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

20 Scopus citations

Abstract

Let G be a finite group, let p be an odd prime, and let P Î Syl_p(G). If N_G(P) = PC_G(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.

Original language	English (US)
Pages (from-to)	1839-1856
Number of pages	18
Journal	Algebra and Number Theory
Volume	8
Issue number	8
DOIs	https://doi.org/10.2140/ant.2014.8.1839
State	Published - 2014
Externally published	Yes

Keywords

McKay conjecture
P-decomposable Sylow normalizer
Self-normalizing Sylow subgroup

ASJC Scopus subject areas

Algebra and Number Theory

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10.2140/ant.2014.8.1839

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title = "Mckay natural correspondences on characters",

abstract = "Let G be a finite group, let p be an odd prime, and let P {\^I} Sylp(G). If NG(P) = PCG(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.",

keywords = "McKay conjecture, P-decomposable Sylow normalizer, Self-normalizing Sylow subgroup",

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

year = "2014",

doi = "10.2140/ant.2014.8.1839",

language = "English (US)",

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pages = "1839--1856",

journal = "Algebra and Number Theory",

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TY - JOUR

T1 - Mckay natural correspondences on characters

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

AU - Vallejo, Carolina

PY - 2014

Y1 - 2014

N2 - Let G be a finite group, let p be an odd prime, and let P Î Sylp(G). If NG(P) = PCG(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.

AB - Let G be a finite group, let p be an odd prime, and let P Î Sylp(G). If NG(P) = PCG(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.

KW - McKay conjecture

KW - P-decomposable Sylow normalizer

KW - Self-normalizing Sylow subgroup

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DO - 10.2140/ant.2014.8.1839

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SP - 1839

EP - 1856

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 8

ER -

Mckay natural correspondences on characters

Abstract

Keywords

ASJC Scopus subject areas

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