  We prove that the class of nilpotent by finite, solvable by finite,
polycyclic by finite, nilpotent of nilpotency class $n$ and supersolvable
groups are closed under the formation of the non-abelian tensor product. We
provide necessary and sufficient conditions for the non-abelian tensor product
of finitely generated groups to be finitely generated. We prove that central
extensions of most finite simple groups have trivial Bogomolov multiplier.
