Automorphism Groups of Wreath Product Digraphs

Automorphism Groups of Wreath Product Digraphs

We strengthen a classical result of Sabidussi giving a necessary and sufficient condition on two graphs, X and Y , for the automorphsim group of the wreath product of the graphs, Aut(X o Y ) to be the wreath product of the automorphism groups Aut(X) o Aut(Y ). We also generalize this to arrive at a similar condition on color digraphs. The main purpose of this paper is to revisit a well-known an...

Wreath products of cyclic p-groups as automorphism groups

We prove that if p is a prime and W is the standard wreath product of two nontrivial cyclic p-groups X and Y then W is isomorphic to the full automorphism group of some group if and only if |X| = 2 and |Y | is 2 or 4.

Automorphism groups of Cayley digraphs of Zp

We calculate the full automorphism group of Cayley digraphs of Zp, p an odd prime, as well as determine the 2-closed subgroups of Sm ≀ Sp with the product action.

Automorphism groups and isomorphisms of Cayley digraphs

Automorphism groups and isomorphisms of Cayley digraphs of Abelian groups

Let S be a minimal generating subset of the finite abelian group G. We prove that if the Sylow 2-subgroup of G is cyclic, then Sand S U S-l are CI-subsets and the corresponding Cayley digraph and graph are normal. Let G be a finite group and let S be a subset of G not containing the identity element 1. The Cayley digraph X = Cay(G, S) of G with respect to S is defined by V(X) = G, E(X) = {(g,sg...