Finite p-groups with the least number of outer p-automorphisms

Abstract

In this paper we study finite [Formula: see text]-groups [Formula: see text] for which the [Formula: see text]-part of [Formula: see text] has the least possible value [Formula: see text]. We characterize the groups in some special cases, including [Formula: see text]-groups of nilpotency class [Formula: see text], of maximal class, of order at most [Formula: see text], with cyclic Frattini subgroup and [Formula: see text]-groups [Formula: see text] in which [Formula: see text].