Characterization of the automorphisms having the lifting property in the category of Abelian \(p\)-groups. (Q1774377)

Summary: Let \(p\) be a prime. It is shown that an automorphism \(\alpha\) of an Abelian \(p\)-group \(A\) lifts to any Abelian \(p\)-group of which \(A\) is a homomorphic image if and only if \(\alpha=\pi\text{id}_A\), with \(\pi\) an invertible \(p\)-adic integer. It is also shown that if \(A\) is a torsion group or a torsion-free \(p\)-divisible group, then \(\text{id}_A\) and \(-\text{id}_A\) are the only automorphisms of \(A\) which possess the lifting property in the category of Abelian groups.