Regular Algebraic $K$-Theory for groups -- Part II

TL;DR

This paper develops the second part of a homology theory for groups called regular algebraic K-theory, which is distinct from ordinary group homology and relates to algebraic K-theory for rings.

Contribution

It extends the theory of regular algebraic K-theory for groups and connects it to algebraic K-theory for rings via a functorial approach.

Findings

Defines a homology theory for discrete groups

Provides a functorial construction for rings

Connects group theory with algebraic K-theory

Abstract

The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from) ordinary group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to the ring $R$ the (perfect) commutator subgroup $E ( R )$ of the infinitedimensional general linear group over $R$.