Generating triples of involutions of alternating groups
type: Item
instance of: scholarly article
title: Generating triples of involutions of alternating groups
zbMATH Open document ID: 0822.20036
DOI: 10.1007/BF01250552
author: Ya. N. Nuzhin
published in: Mathematical Notes
publication date: 1994-02-08T00:00:00Z
review text: Mazurov asked the question: Which (known) finite simple groups are generated by three involutions, two of which commute? The answer to this question is known for Chevalley groups of rank 1 and for Chevalley groups over a field of characteristic 2. Here we will prove Theorem 1: The alternating group \(A_ n\) is generated by three involutions \(t\), \(u\), \(v\), the first two of which commute, if and only if \(n \geq 9\) or \(n = 5\).
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20E26
zbMATH DE Number: 484287
zbMATH Keywords: finite simple groups
zbMATH Keywords: generated by three involutions
zbMATH Keywords: alternating groups
MaRDI profile type: Publication
cites work: Structure of Lie type groups of rank 1
cites work: Hereditary and semihereditary rings without nilpotent elements
cites work: Generators for Alternating and Symmetric Groups
cites work: MORE ON GENERATORS FOR ALTERNATING AND SYMMETRIC GROUPS
cites work: Q3855356
Recommended article: Generating triples of involutions of large sporadic groups
Recommended article: Q5147361
Recommended article: Generating triples of involutions of groups of Lie type of rank 2 over finite fields
Recommended article: Q5263754
Recommended article: Generating triples of involutions of Chevalley groups over a finite field of characteristic 2
Recommended article: Generation of some orthogonal groups by a set of three involutions
Recommended article: Q3795835
Recommended article: Q3825230
Recommended article: Generation of alternating groups by pairs of conjugates
Recommended article: On the generation of Coxeter groups and their alternating subgroups by involutions
description: scientific article; zbMATH DE number 484287