Infinite metacyclic groups and their non-abelian tensor squares

In this paper we classify ail infinite metacyclic groups up to isomorphism and determine their non-abelian tensor squares. As an application we comput e various other functors, among them are the exterior square, the symmetric product, and the second homology group for these groups. We show that an i nfinite non-abelian metacyclic group is capable if and only if it is isomor phic to the infinite dihedral group.