Restricted-finite groups with some applications in group rings (Q6595647)

In this paper, a group \(G\) is called restricted-finite if \(|G:H|\) is finite for any non-trivial infinite subgroup \(H\) of \(G\). The authors give several standard examples and some of the properties of such groups including the facts that restricted-finite groups are countable and a non-trivial torsion-free restricted-finite group must be isomorphic to \(\mathbb{Z}\). A characterization is also given of restricted finite groups in which the derived subgroup is finite and of infinite abelian such groups. Infinitely generated restricted-finite groups are also characterized. Some work is also done concerning group rings of such groups.