Automorphism groups of tetravalent Cayley graphs on regular p-groups

Let Cay(G, S) be a connected tetravalent Cayley graph on a regular p-group G and let Aut(G) be the automorphism group of G. In this paper, it is proved that, for each prime p 5 2, 5, the automorphism group of the Cayley graph Cay(G, S) is the semidirect product R(G) x Aut(G, S) where R(G) is the right regular representation of G and Aut(G, S) = (alpha is an element of Aut(G)vertical bar S-alpha = S). The proof depends on the classification of finite simple groups. This implies that if p A 2, 5 then the Cayley graph Cay(G, S) is normal, namely, the automorphism group of Cay(G, S) contains R(G) as a normal subgroup. (c) 2005 Elsevier B.V. All rights reserved.