The ideal class group action on K-groups and homology groups

Abstract

In this paper, for an extension of rings R⊆R′, consider Nn the normalizer of GLn(R) in GLn(R′). We study the action of Nn on the homology groups of GLn(R) and K-groups of R induced by the conjugation action, and relate it to the n-torsion of the ideal class group of R in case R is a Dedekind domain.