A unit group in a character ring of an alternating group. II
type: Item
instance of: scholarly article
title: A unit group in a character ring of an alternating group. II
zbMATH Open document ID: 0814.20008
author: Kenichi Yamauchi
published in: Hokkaido Mathematical Journal
publication date: 1993-05-16T00:00:00Z
review text: This paper is a continuation of part I [ibid. 20, No. 3, 549-558 (1991)] in which the author showed that the factor group \(U(R(A_ n))/\{\pm 1\}\) is a free abelian group of rank \(c(n)\) [see the preceding review Zbl 0814.20007 for the notations]. In the present paper, the author constructs \(c(n)\) elements \(\psi_ 1,\dots,\psi_{c(n)}\) in \(U(R(A_ n))\) such that the subgroup of \(U(R(A_ n))\) generated by these elements has rank \(c(n)\) and contains \(\{\psi^ 2 \mid \psi \in U(R(A_ n))\}\) as is subset. The author also gives a necessary and sufficient condition on an element \(\psi \in U(R(A_ n))\) to be the difference of two irreducible complex characters of \(A_ n\).
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 19A22
zbMATH DE Number: 165207
zbMATH Keywords: alternating groups
zbMATH Keywords: unit group
zbMATH Keywords: character rings
zbMATH Keywords: irreducible complex characters
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381413120
OpenAlex ID: W4253031881
DOI: 10.14492/HOKMJ/1381413120
description: scientific article; zbMATH DE number 165207