The CI problem for infinite groups

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dc.contributor.authorMorris, Joy
dc.date.accessioned2018-06-29T17:50:18Z
dc.date.available2018-06-29T17:50:18Z
dc.date.issued2016
dc.descriptionSherpa Romeo green journal: open accessen_US
dc.description.abstractA finite group G is a DCI-group if, whenever S and S0 are subsets of G with the Cayley graphs Cay(G,S) and Cay(G,S0) isomorphic, there exists an automorphism ϕ of G with ϕ(S) = S0. It is a CI-group if this condition holds under the restricted assumption that S = S−1. We extend these definitions to infinite groups, and make two closely-related definitions: an infinite group is a strongly (D)CIf-group if the same condition holds under the restricted assumption that S is finite; and an infinite group is a (D)CIf-group if the same condition holds whenever S is both finite and generates G. We prove that an infinite (D)CI-group must be a torsion group that is not locallyfinite. We find infinite families of groups that are (D)CIf-groups but not strongly (D)CIf-groups, and that are strongly (D)CIf-groups but not (D)CI-groups. We discuss which of these properties are inherited by subgroups. Finally, we completely characterise the locally-finite DCI-graphs on Zn. We suggest several open problems related to these ideas, including the question of whether or not any infinite (D)CIgroup exists.en_US
dc.description.peer-reviewYesen_US
dc.identifier.citationMorris, J. (2016). The CI problem for infinite groups. Electronic Journal of Combinatorics, 23(4), 4.37en_US
dc.identifier.urihttps://hdl.handle.net/10133/5145
dc.language.isoen_USen_US
dc.publisherElectronic Journal of Combinatoricsen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.publisher.institutionUniversity of Lethbridgeen_US
dc.subjectCaleyen_US
dc.subjectIsomorphismsen_US
dc.subjectInfinite groupsen_US
dc.subjectCI-problemen_US
dc.subjectCI-groupen_US
dc.subjectCI-graphen_US
dc.subject.lcshIsomorphisms (Mathematics)
dc.subject.lcshCaley graphs
dc.subject.lcshCombinatorial analysis
dc.subject.lcshGroup theory
dc.titleThe CI problem for infinite groupsen_US
dc.typeArticleen_US
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