The automorphism group of finite $p$-abelian $p$-groups

If n is an integer, a group G is called n-Abelian if (xy)" x'y for all ele- ments x, y of G.It is immediate that, for each integer n, the class of n-Abelian groups forms a variety which contains the variety of Abelian groups as a subvariety.F. Levi [8], O. Grfin [5] and R. Baer [2], [3] have developed theory pertaining to n-Abelian groups for arbitrary groups.In this paper we restrict our attention to the class of finite p-Abelian p-groups, where p is a prime number.It should be noted that each p-Abelian p-group is trivially a regular p-group and also that each p-group of exponent p is a p-Abelian p-group.