Field equivalent finite groups.
type: Item
instance of: scholarly article
title: Field equivalent finite groups.
zbMATH Open document ID: 1077.20011
author: Alexander Moretó
author: Gabriel Navarro
published in: Mathematische Zeitschrift
publication date: 2005-02-02T00:00:00Z
review text: Following a suggestion of I. M. Isaacs, the authors define two finite groups \(X\) and \(Y\) to be `field equivalent' if there is a bijection \(\chi\to\chi'\) from the set of all irreducible characters of \(X\) to the set of all irreducible characters of \(Y\) such that, for every \(\chi\), the fields of values over the rational numbers of \(\chi\) and of \(\chi'\) are equal, so that \(\mathbb{Q}(\chi)=\mathbb{Q}(\chi')\). The authors prove that if \(G\) is a finite group which is field equivalent to a cyclic group, then \(G\) is a cyclic group. They remark that there exist non-Abelian groups which are field equivalent to elementary Abelian groups, and non-solvable groups which are field equivalent to \(2\)-groups.
reviewed by: Alexandre Turull
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 2132005
zbMATH Keywords: finite cyclic groups
zbMATH Keywords: irreducible complex characters
zbMATH Keywords: rational-valued irreducible characters
zbMATH Keywords: field equivalent groups
zbMATH Keywords: numbers of characters
MaRDI profile type: Publication
full work available at URL: s00209-004-0681-9
OpenAlex ID: W2010463663
cites work: A Note on Finite Groups with an Abelian Sylow Group
cites work: Characters of Solvable and Symplectic Groups
cites work: Q4871631
cites work: On finite groups with exactly two real conjugate classes
cites work: Q4273959
cites work: On finite automorphic algebras
DOI: 10.1007/S00209-004-0681-9
description: scientific article; zbMATH DE number 2132005