Sharp characters of finite groups of type \(\{-1,1\}\)
type: Item
instance of: scholarly article
title: Sharp characters of finite groups of type \(\{-1,1\}\)
zbMATH Open document ID: 0776.20002
DOI: 10.1016/0021-8693(92)90099-8
author: Peter J. Cameron
author: Toshitaka Kataoka
author: Masao Kiyota
published in: Journal of Algebra
publication date: 1993-03-29T00:00:00Z
review text: It is known that \(|{\mathcal G}|\) divides \(\prod_{t\in T} (n-t)\), where \(n=\chi(1)\), \(\chi\) a virtual character of the finite group \({\mathcal G}\), \(T=\{\chi(g)\); \(g\in{\mathcal G}\setminus\{1\}\}\). This is a result proved by Blichfeldt, Cameron and Kiyota, Hekster. Note that indeed \(\prod_{t\in T} (n-t)\in\mathbb{Z}\). If \(|{\mathcal G}|=\prod_{t\in T} (n-t)\), then we say that \(\chi\) is sharp of type \(T\). In this paper the groups \({\mathcal G}\) are determined admitting \(\chi\in \text{char}({\mathcal G})\) that are sharp of type \(\{-1,+1\}\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 130498
zbMATH Keywords: sharp characters
zbMATH Keywords: virtual characters
zbMATH Keywords: finite groups
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: 0021-8693(92)90099-8
OpenAlex ID: W2053661211
cites work: Finite Groups with Quasi-Dihedral and Wreathed Sylow 2-Subgroups
cites work: Sharp characters of finite groups
cites work: The characterization of finite groups with dihedral Sylow 2-subgroups. III
cites work: Sharp permutation groups
description: scientific article; zbMATH DE number 130498