Name
Abstract | ||
|---|---|---|
We say that a finite group G is "DRR-detecting" if, for every subset S of G, either the Cayley digraph Cay(G,S) is a digraphical regular representation (that is, its automorphism group acts regularly on its vertex set) or there is a nontrivial group automorphism phi of G such that phi(S) = S. We show that every nilpotent DRR-detecting group is a p-group, but that the wreath product of two cyclic groups of order p is not DRR-detecting, for every odd prime p. We also show that if G and H are nontrivial groups that admit a digraphical regular representation and either gcd(|G|,|H|) = 1, or H is not DRR-detecting, then the direct product G x H is not DRR-detecting. Some of these results also have analogues for graphical regular representations. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.26493/2590-9770.1373.60a | The Art of Discrete and Applied Mathematics |
DocType | Volume | Issue |
Journal | 5 | 1 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dave Witte Morris | 1 | 20 | 5.42 |
| Joy Morris | 2 | 78 | 16.06 |
| Verret Gabriel | 3 | 0 | 0.34 |