The non-isolated vertices in the generating graph of a direct powers of simple groups.
type: Item
instance of: scholarly article
title: The non-isolated vertices in the generating graph of a direct powers of simple groups.
zbMATH Open document ID: 1276.20026
author: Eleonora Crestani
author: Andrea Lucchini
published in: Journal of Algebraic Combinatorics
publication date: 2013-02-15T00:00:00Z
review text: Let \(G\) be a finite group. The generating graph \(L(G)\) of \(G\) has its vertices the set of non-identity elements of \(G\) where two vertices are joined if and only if they generate the group \(G\). Many properties of the group \(G\) can equivalently be stated in terms of \(L(G)\). In the paper under review the authors consider a finite non-Abelian simple group \(G\) and let \(G^d\) be the largest 2-generated power of \(G\), and study behavior of \(L(G^d)\) with respect to that of \(L(G)\).
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 6136609
zbMATH Keywords: finite groups
zbMATH Keywords: generating graphs
zbMATH Keywords: 2-generator groups
zbMATH Keywords: direct powers of simple groups
zbMATH Keywords: diameters of graphs
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: s10801-012-0365-1
OpenAlex ID: W1964770012
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DOI: 10.1007/S10801-012-0365-1
description: scientific article; zbMATH DE number 6136609