Rational irreducible characters and rational conjugacy classes in finite groups

Gabriel Navarro; Pham Huu Tiep

doi:10.1090/S0002-9947-07-04375-9

Rational irreducible characters and rational conjugacy classes in finite groups

Gabriel Navarro
, Pham Huu Tiep

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

65 Scopus citations

Abstract

We prove that a finite group G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rationalvalued irreducible character of odd degree.

Original language	English (US)
Pages (from-to)	2443-2465
Number of pages	23
Journal	Transactions of the American Mathematical Society
Volume	360
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9947-07-04375-9
State	Published - May 2008
Externally published	Yes

Keywords

Rational conjugacy class
Rational irreducible character

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-07-04375-9

Cite this

@article{f391436952a640b7a9eea7f620067d59,

title = "Rational irreducible characters and rational conjugacy classes in finite groups",

abstract = "We prove that a finite group G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rationalvalued irreducible character of odd degree.",

keywords = "Rational conjugacy class, Rational irreducible character",

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

year = "2008",

month = may,

doi = "10.1090/S0002-9947-07-04375-9",

language = "English (US)",

volume = "360",

pages = "2443--2465",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "5",

}

TY - JOUR

T1 - Rational irreducible characters and rational conjugacy classes in finite groups

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

PY - 2008/5

Y1 - 2008/5

N2 - We prove that a finite group G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rationalvalued irreducible character of odd degree.

AB - We prove that a finite group G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rationalvalued irreducible character of odd degree.

KW - Rational conjugacy class

KW - Rational irreducible character

UR - https://www.scopus.com/pages/publications/47749101784

UR - https://www.scopus.com/pages/publications/47749101784#tab=citedBy

U2 - 10.1090/S0002-9947-07-04375-9

DO - 10.1090/S0002-9947-07-04375-9

M3 - Article

AN - SCOPUS:47749101784

SN - 0002-9947

VL - 360

SP - 2443

EP - 2465

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 5

ER -

Rational irreducible characters and rational conjugacy classes in finite groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this