Multiple holomorphs of finite p-groups of class two

More generally, we develop some aspects of a theory of T(G) for G a finite p-group of class 2, for p>2. In particular, we show that for such a group G there is an element of order p−1 in T(G), and exhibit examples where |T(G)|=p−1, and others where T(G) contains a large elementary abelian p-subgroup.