Russell D. Blyth, Francesco Fumagalli, Marta Morigi
July 14, 2009
We study the non-abelian tensor square G ⊗ G for the class of groups G that are finitely generated modulo their derived subgroup. In particular, we find conditions on G / G ′ so that G ⊗ G is isomorphic to the direct product of ∇( G ) and the non-abelian exterior square G ∧ G . For any group G , we characterize the non-abelian exterior square G ∧ G in terms of a presentation of G . Finally, we apply our results to some classes of groups, such as the classes of free solvable and free nilpotent groups of finite rank, and some classes of finite p -groups.