Central automorphisms and inner automorphisms of nilpotent groups with the minimal condition on subgroups

Let [Formula: see text] be a group and [Formula: see text] the group of all central automorphisms of [Formula: see text]. Denote by [Formula: see text] the group of all central automorphisms of [Formula: see text] fixing [Formula: see text] elementwise. We characterize all nilpotent groups [Formula: see text] of class 2 with the minimal condition on subgroups for which [Formula: see text]. Let [Formula: see text] be a central product of a finitely generated nilpotent group and a nilpotent group with the minimal condition on subgroups. When the nilpotency class of [Formula: see text] is 2, we characterize [Formula: see text] for which [Formula: see text].