On twisted group C$^*$-algebras associated with FC-hypercentral groups   and other related groups
  We show that the twisted group C$^*$-algebra associated with a discrete FC-hypercentral group is simple (resp. has a unique tracial state) if and only if Kleppner's condition is satisfied. This generalizes a result of J. Packer for countable nilpotent groups. We also consider a larger class of groups, for which we can show that the corresponding reduced twisted group C$^*$-algebras have a unique tracial state if and only if Kleppner's condition holds. 
Erik Bedos, Tron Omland
math.OA math.GR