Generating alternating groups
type: Item
instance of: scholarly article
title: Generating alternating groups
zbMATH Open document ID: 0891.20003
author: Naoki Chigira
published in: Hokkaido Mathematical Journal
publication date: 1998-07-19T00:00:00Z
review text: The starting point of this paper is the claim that for any non-identity element \(x\) of the alternating group \(A_n\) there is \(y\in A_n\) such that \(\langle x,y\rangle=A_n\), made by \textit{I. M. Isaacs} and \textit{T. Zieschang} [Am. Math. Mon. 102, No. 8, 734-739 (1995; Zbl 0846.20004)]. A proof of this theorem is given here. It uses some lemmas from the aforementioned paper, the Jordan theorem on 3-cycles and a detailed analysis of the behaviour of imprimitivity blocks.
Mathematics Subject Classification ID: 20B35
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20B15
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 1054037
zbMATH Keywords: two-generated groups
zbMATH Keywords: alternating groups
zbMATH Keywords: imprimitivity blocks
reviewed by: Raffaele Scapellato
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351257975
OpenAlex ID: W2043198265
DOI: 10.14492/HOKMJ/1351257975
description: scientific article; zbMATH DE number 1054037