Characterization of the automorphisms having the lifting property in the category of abelian p-groups

Abstract

Let p be a prime. It is shown that an automorphism α of an abelian p-group A lifts to any abelian p-group of which A is a homomorphic image if and only if α=π idA, with π an invertible p-adic integer. It is also shown that if A is torsion group or torsion-free p-divisible group, then idA and −idA are the only automorphisms of A which possess the lifting property in the category of abelian groups.