Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups

Show simple item record

dc.contributor.author Verret G
dc.contributor.author Morgan L
dc.contributor.author Morris J
dc.date.accessioned 2020-11-13T03:09:59Z
dc.date.available 2020-11-13T03:09:59Z
dc.date.issued 2020-1-9
dc.identifier.uri http://hdl.handle.net/2292/53626
dc.description.abstract Let Γ = Cay(G, S) be a Cayley digraph on a group G and let A = Aut(Γ). The Cayley index of Γ is |A : G|. It has previously been shown that, if p is a prime, G is a cyclic p-group and A contains a noncyclic regular subgroup, then the Cayley index of Γ is superexponential in p. We present evidence suggesting that cyclic groups are exceptional in this respect. Specifically, we establish the contrasting result that, if p is an odd prime and G is abelian but not cyclic, and has order a power of p at least p3, then there is a Cayley digraph Γ on G whose Cayley index is just p, and whose automorphism group contains a nonabelian regular subgroup.
dc.relation.ispartofseries The Art of Discrete and Applied Mathematics
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
dc.title Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups
dc.type Journal Article
dc.identifier.doi 10.26493/2590-9770.1254.266
pubs.issue 1
pubs.begin-page 1
pubs.volume 3
dc.date.updated 2020-10-12T02:12:03Z
dc.rights.holder Copyright: The author en
pubs.author-url https://adam-journal.eu/index.php/ADAM/article/view/1254
pubs.end-page 1
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Article
pubs.elements-id 817852
pubs.online-publication-date 2020-1-9

Files in this item

Find Full text

This item appears in the following Collection(s)

Show simple item record


Search ResearchSpace