Abstract:

We establish some additional results concerning relatively co-Hopfian Abelian groups, recently defined by us in the Siber. Math. J. (2026). Concretely, for any prime $p$, we prove that relatively co-Hopfian $p$-groups are thick as well as that separable relatively co-Hopfian $p$-groups are thin. Moreover, we show that a reduced fully-starred $p$-group is relatively co-Hopfian exactly when it is finite. Finally, we demonstrate that relatively co-Hopfian groups are closed under the formation of finitely generated extension.