Real ordinary characters and real brauer characters

Pham Huu Tiep

doi:10.1090/s0002-9947-2014-06148-5

Real ordinary characters and real brauer characters

Pham Huu Tiep

Mathematics

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

12 Scopus citations

Abstract

We prove that if G is a finite group and p is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible p-Brauer character, of G is coprime to p, then O^p'(G) is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator 1.

Original language	English (US)
Pages (from-to)	1273-1312
Number of pages	40
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	2
DOIs	https://doi.org/10.1090/s0002-9947-2014-06148-5
State	Published - 2015

Keywords

Frobenius-Schur indicator
Real-valued Brauer characters
Real-valued ordinary characters

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9947-2014-06148-5

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title = "Real ordinary characters and real brauer characters",

abstract = "We prove that if G is a finite group and p is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible p-Brauer character, of G is coprime to p, then Op'(G) is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator 1.",

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N2 - We prove that if G is a finite group and p is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible p-Brauer character, of G is coprime to p, then Op'(G) is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator 1.

AB - We prove that if G is a finite group and p is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible p-Brauer character, of G is coprime to p, then Op'(G) is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator 1.

KW - Frobenius-Schur indicator

KW - Real-valued Brauer characters

KW - Real-valued ordinary characters

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UR - https://www.scopus.com/pages/publications/84928241070#tab=citedBy

U2 - 10.1090/s0002-9947-2014-06148-5

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -

Real ordinary characters and real brauer characters

Abstract

Keywords

ASJC Scopus subject areas

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