Projective modules, augmentation and idempotents in group algebras

We consider a condition on a group G, that was studied by Strebel and independently by Strojnowski, which implies that the complex group algebra of G has no non-trivial idempotents. We elaborate on that technique and slightly relax the Strebel–Strojnowski condition. This enables us to prove in a relatively simple way certain closure properties for the resulting class of groups.