AUTOMORPHISM GROUPS OF 4-VALENT CONNECTED CAYLEY GRAPHS OF p-GROUPS~****

摘要

Let G be a p-group (p odd prime) and let X=Cay(G,S) be a 4-valent connected Cayley graph. It is shown that if G has nipotent class 2, then the automorphism group Aut(X) of X is isomorphic to the semidirect product G_R Aut (G, S), where G_R is the right regular Representation of G and Aut(G,S) is the subgroup of the automorphism group Aut(G) of G Which fixes S setwise. However the result is not true if G has nilpotent class 3 and this paper Provides a counterexample.