On the Cayley isomorphism problem for ternary relational structures
type: Item
instance of: scholarly article
title: On the Cayley isomorphism problem for ternary relational structures
zbMATH Open document ID: 1028.05069
DOI: 10.1016/S0097-3165(02)00014-6
author: Edward Dobson
published in: Journal of Combinatorial Theory. Series A
publication date: 2003-04-28T00:00:00Z
review text: The Cayley isomorphism problem asks for which groups \(G\) it is true that every two Cayley objects of \(G\) are isomorphic if and only if they are isomorphic by a group isomorphism of \(G\). Such groups are called CI-groups with respect to the underlying class of combinatorial objects. The objects considered here are ternary relational structures. A list of all possible CI-groups with respect to color ternary relational structures is provided. Of those, the groups of order \(2n\) and \(4n\) with a cyclic Sylow 2-subgroup are either shown to be CI-groups as is the case for most of them, or, in the unresolved cases necessary and sufficient conditions for the group to be a CI-group with respect to ternary relational structures are provided. Since a CI-group with respect to ternary relational structures is also a CI-group with respect to binary relational structures, some of the examined groups provide new examples of CI-groups with respect to graphs and digraphs.
reviewed by: Brigitte Servatius
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 08A02
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 1902848
zbMATH Keywords: ternary relational structure
zbMATH Keywords: Cayley isomorphism
zbMATH Keywords: CI-group
MaRDI profile type: Publication
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full work available at URL: s0097-3165(02)00014-6
OpenAlex ID: W2048039498
description: scientific article; zbMATH DE number 1902848