Crossed group rings with a finite set of degrees of indecomposable representations over Dedekind domains (Q2777548)

Let \(S\) be a Dedekind domain of characteristic \(p>0\) dividing the order of the finite group \(G\), and let \(S^\lambda G\) be the crossed group ring (twisted group algebra) of \(G\) and \(S\) with factor set \(\lambda\). Denote by \(D(S^\lambda G)\) the set of degrees of all indecomposable matrix \(S\)-representations \(\Gamma\colon S^\lambda G\to M_n(S)\). Building on earlier work of S.~D.~Berman, P.~M.~Gudivok and others, the authors give necessary conditions for the finiteness of \(D(S^\lambda G)\) for any \(S\) as above. Then necessary and sufficient conditions are obtained when \(S\) is the ring \(F[x]\) of polynomials over a field \(F\), and when \(S\) is the ring \(F[[x]]\) of formal power series over the field \(F\) and \(\lambda\in Z^2(G,F^*)\). (Also submitted to MR).