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

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dc.contributor.authorMorgan, Luke
dc.contributor.authorMorris, Joy
dc.contributor.authorVerret, Gabriel
dc.date.accessioned2025-12-13T21:34:33Z
dc.date.available2025-12-13T21:34:33Z
dc.date.issued2020
dc.descriptionOpen access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
dc.description.abstractLet 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.description.peer-reviewYes
dc.identifier.citationMorgan, L., Morris, J., & Verret, G. (2020). Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups. The Art of Discrete and Applied Mathematics, 3, Article #P1.01. https://doi.org/10.26493/2590-9770.1254.266
dc.identifier.urihttps://hdl.handle.net/10133/7259
dc.language.isoen
dc.publisherUniversity of Primorska
dc.publisherThe Slovenian Discrete and Applied Mathematics Society
dc.publisher.departmentDepartment of Mathematics and Computer Science
dc.publisher.facultyArts and Science
dc.publisher.institutionUniversity of Western Australia
dc.publisher.institutionUniversity of Lethbridge
dc.publisher.institutionUniversity of Auckland
dc.publisher.urlhttps://doi.org/10.26493/2590-9770.1254.266
dc.subjectCayley digraphs
dc.subjectCayley index
dc.subjectAutomorphism
dc.subjectNonisomorphic
dc.titleDigraphs with small automorphism groups that are Cayley on two nonisomorphic groups
dc.typeArticle
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