Simplicial methods and the homology of groups.

Abstract

This thesis generalizes the simplicial methods of defining derived functors and proves characterization theorems about them. In particular, we show that our methods also generalize an alternative way of defining derived functors, We use our definitions to define the higher Baer invariants of a group relative to a variety of groups and compute them in special cases. Finally, we deduce a long exact sequence in the homology of groups.