This paper deals with the determination of the automorphism group of the metacyclic p-groups, P (p,m), given by the presentation P (p,m) = 〈x, y|xpm = 1, y = 1, yxy−1 = xp+1〉 (1) where p is an odd prime number and m > 1. We will show that Aut(P ) has a unique Sylow p-subgroup, Sp, and that in fact
