Nonabelian tensor products and nonabelian homology of groups

Abstract

The non-abelian tensor product of groups introduced by Brown and Loday is generalized. The homology groups of groups are constructed with coefficients in any group, as the left derived functors of the non-abelian tensor product, which generalize the classical theory of homology of groups. Exact sequences of the non-abelian homology groups and their application to algebraic K-theory of noncommutative local rings are given.