On Abelian groups with commuting monomorphisms. (Q392745)

In the present paper the author studies Abelian groups \(G\) with the property that for any two monomorphisms \(f,g\colon G\to G\) we have \(fg=gf\). He obtains many interesting connections between these groups and other classes of Abelian groups, as Abelian groups with central idempotents (Theorem 1) or co-Hopfian groups (Theorem 2). The author also studies a related question: when are all monomorphisms left or right invariant?