When amenable groups have real rank zero C∗-algebras

Abstract

We investigate when discrete, amenable groups have [Formula: see text]-algebras of real rank zero. While it is known that this happens when the group is locally finite, the converse is an open problem. We show that if [Formula: see text] has real rank zero, then all normal subgroups of [Formula: see text] that are elementary amenable and have finite Hirsch length must be locally finite.