Projective Modules over Finite Groups

Serre [5] has recently proved a general theorem about projective modules over commutative rings. This theorem has the following consequence : If 7T is a finite abelian group, any finitely generated projective module over the integral group ring Zir is the direct sum of a free module and an ideal of Zir. The question naturally arises as to whether this result holds for nonabelian groups x. Serre's methods rely heavily on commutativity and do not seem to generalize to the nonabelian case. However, by using different methods, I have been able to prove the following theorem which generalizes Serre's result even for abelian groups.