Eine Charakterisierung Gewisser Diskreter Gruppen Durch Ihre Reguläre Darstellung

Let W(G) be the W^{{star operator}}-algebra generated by the left regular representation of a discrete group G. We discuss the relationship between minimal central idempotents of W(G) and certain positiv definit functions on G. As a main result we get a characterisation of those groups G for which W(G)_I ≠ {O} and W(G)_II is a direct product of factors. If one includes the case W(G)_II={O} these are precisely finite extensions of groups H, where H is abelian or nilpotent of class 2 with finite center and commutatorsubgroup of prime order.