Name
Abstract | ||
|---|---|---|
Let $Gamma=mathrm{Cay}(G,S)$ be a Cayley digraph on a group $G$ and let $A=mathrm{Aut}(Gamma)$. The Cayley index of $Gamma$ 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 $Gamma$ 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 $p^3$, then there is a Cayley digraph $Gamma$ on $G$ whose Cayley index is just $p$, and whose automorphism group contains a nonabelian regular subgroup. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.26493/2590-9770.1254.266 | Art Discret. Appl. Math. |
DocType | Volume | Issue |
Journal | 3 | 1 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Luke Morgan | 1 | 2 | 2.13 |
| Joy Morris | 2 | 78 | 16.06 |
| Gabriel Verret | 3 | 56 | 9.25 |