On mixed Abelian groups with periodic groups of automorphisms (Q1274017)

The author studies mixed abelian groups \(G\) whose automorphism groups \(\Aut(G)\) contain no element of infinite order. The main results are sufficient conditions on \(G\) and \(\Aut(G)\) for \(G\) to split as a direct sum of its torsion and torsion-free parts. For example, it is shown that if \(\Aut(G)\) is finite, then \(G\) always splits. In the second half of the paper, the author finds sufficient conditions on \(G\) for its holomorph to be perfect.