Automorphism groups and isomorphisms of Cayley digraphs
type: Item
instance of: scholarly article
title: Automorphism groups and isomorphisms of Cayley digraphs
zbMATH Open document ID: 0887.05025
DOI: 10.1016/S0012-365X(97)00152-0
published in: Discrete Mathematics
publication date: 1998-03-24T00:00:00Z
review text: Let \(G\) be a finite group and \(S\) a subset of \(G\), not containing the identity element 1. The Cayley digraph \(X=\text{Cay} (G,S)\) is defined by \(V(X)=G\) and \(E(X)=\{(g,sg)\;|\;g\in G,\;s\in S\}\). A subset \(S\) of \(G\) is called a CI-subset of \(G\), if for any subset \(T\) of \(G\) with \(\text{Cay} (G,S)\) isomorphic to \(\text{Cay} (G,T)\), there exists \(\alpha \in\Aut(G)\) such that \(S^\alpha=T\). A number of results on Cayley digraphs is obtained, for example, Proposition 3.5: Let \(G\) be a finite group and \(p\) the least divisor of \(|G|\). Let \(S\) be a generating set of \(G\) with \(|S|<p\). Then \(S\) is a CI-subset.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 1121505
zbMATH Keywords: Cayley digraph,
zbMATH Keywords: CI-subset of group
author: Mingyao Xu
reviewed by: Alexandre A. Makhnev
MaRDI profile type: Publication
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full work available at URL: s0012-365x(97)00152-0
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description: scientific article; zbMATH DE number 1121505