Presentations of some finite groups with applications to the O'Nan simple group
type: Item
instance of: scholarly article
title: Presentations of some finite groups with applications to the O'Nan simple group
zbMATH Open document ID: 0615.20016
DOI: 10.1016/0021-8693(87)90104-9
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The author gives presentations for the groups \(S_ 5\), \(L_ 2(11)\), \(M_{11}\), \(M_{12}:2\), \(J_ 1\), and \(12\cdot L_ 3(4):2\) and presentations for groups G, H with \([H:G]=2\) which have \(3\cdot O'N\) resp. \(3\cdot O'N:2\) as epimorphic images. The generators represent involutions, the relations give the ''orders'' of the products of two generators as for Coxeter groups and are supplemented by further relations like \((bc)^ 2=a\) or \((abc)^ 5=1\). The proofs use coset enumeration by a computer with respect to a previously identified subgroup generated by some of the generators. The enumeration for \([H:G]=2\) needs space for 5000 cosets.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 3995961
zbMATH Keywords: Janko group
zbMATH Keywords: O'Nan group
zbMATH Keywords: Mathieu groups
zbMATH Keywords: presentations
zbMATH Keywords: generators
zbMATH Keywords: involutions
zbMATH Keywords: relations
zbMATH Keywords: Coxeter groups
zbMATH Keywords: coset enumeration
author: Leonard H. Soicher
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90104-9
OpenAlex ID: W1993859829
cites work: Q3728814
cites work: Q3684278
cites work: A new combinatorial approach to M24
cites work: Some Evidence for the Existence of a New Simple Group
cites work: A new construction of the O'Nan simple group
cites work: The maximal subgroups of the O'Nan group
description: scientific article; zbMATH DE number 3995961