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

摘要

In this paper we study finite p-groups G for which the p-part of vertical bar Aut(G) : Inn( G)vertical bar has the least possible value p. We characterize the groups in some special cases, including p-groups of nilpotency class 2, of maximal class, of order at most p(5), with cyclic Frattini subgroup and p-groups G in which vertical bar G : Z(G)vertical bar <= p(4).