Projective representations and relative semisimplicity (Q1305078)

Let \(R=\mathbb{Z}/p^s\mathbb{Z}\) for some \(s\geq 2\) and some prime \(p\). The authors characterize finite groups \(G\) with the property that, for some \(\alpha\in H^2(G,R^*)\), all lattices over the twisted group ring \(R^\alpha G\) are projective. If \(p\) is odd then such groups are \(p\)-nilpotent with cyclic Sylow \(p\)-subgroups while in case \(p=2\) cyclic or dihedral Sylow 2-subgroups may occur.