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

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Date
2020
Authors
Morgan, Luke
Morris, Joy
Verret, Gabriel
Journal Title
Journal ISSN
Volume Title
Publisher
University of Primorska
The Slovenian Discrete and Applied Mathematics Society
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.
Description
Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Cayley digraphs , Cayley index , Automorphism , Nonisomorphic
Citation
Morgan, 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
URI
https://hdl.handle.net/10133/7259
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Morris, Joy