Amenable groups of finite cohomological dimension and the zero divisor   conjecture
  We prove that every amenable group of cohomological dimension two whose integral group ring is a domain is solvable and investigate certain homological finiteness properties of groups that satisfy the analytic zero divisor conjecture and act on an acyclic CW-complex with amenable stabilisers. 
Dieter Degrijse
math.GR math.FA