Universal Central Extensions of Internal Crossed Modules via the Non-abelian Tensor Product

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

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...

On universal central extensions of precrossed and crossed modules

Central extensions of precrossed and crossed modules

The notion of centrality for crossed modules was introduced by Norrie in her thesis [7], in which she studied the category of crossed modules CM from an algebraic point of view, showing suitable generalizations of group theoretic concepts and results. Subsequently, Norrie’s approach was followed by Carrasco, Cegarra and R.-Grandjeán. In [5] they proved that CM is an algebraic category (i.e. the...

Fe b 20 07 Prime to p extensions of the generic abelian crossed product

In this paper we prove that the noncyclic generic abelian crossed product p-algebras constructed by Amitsur and Saltman in [AS78] remain noncyclic after tensoring by any prime to p extension of their centers. We also prove that an example due to Saltman of an indecomposable generic abelian crossed product with exponent p and degree p 2 remains indecomposable after any prime to p extension. 0 In...

Finiteness of a Non Abelian Tensor Product of Groups

Some su cient conditions for niteness of a generalized non abelian tensor product of groups are established extending Ellis result for compatible actions The non abelian tensor product of groups was introduced by Brown and Loday following works of A Lue and R K Dennis It was de ned for any groups A and B which act on themselves by conjugation y xyx and each of which acts on the other such that ...