The group of outer automorphisms of an infinite nilpotent p-group and its normal p-subgroups (Q1073183)

This paper is a contribution to the literature on normal p-subgroups of the automorphism groups of p-groups. The finite case was dealt with by Peter Schmid. Here it is shown that if G is an infinite nilpotent p-group and Out G has no non-identity normal p-subgroup, then there are three possibilities. (1) G is elementary Abelian. (2) G is divisible and p is odd. (3) G is the central product of P and C, where P is a finite extraspecial group of exponent \(p\neq 2\) and C is a quasicyclic p-group. The proof owes some details to a paper of Menegazzo and Stonehewer.