The non-abelian tensor product of normal crossed submodules of groups

Abstract. In this article, the notions of non-abelian tensor and exterior
products of two normal crossed submodules of a given crossed module of
groups are introduced and some of their basic properties are established. In
particular, we investigate some common properties between normal crossed
modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the tensor product, provided such information is given at least on one of the normal crossed submodules.

The non-abelian tensor product of normal crossed submodules of groups Keywords:

crossed module , tensor product , exterior product