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

Document Type: Research Paper


Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran 19839, Iran.


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.


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