Isomorphism of commutative modular twisted group algebras. (Q1887400)

Let \(A\) be an Abelian group, \(R\) a commutative ring with \(1\) and \(R_tA\) a commutative twisted group algebra. It is proved that if \(R_tA\) is isomorphic as an \(R\)-algebra to a twisted group algebra \(R_{t_1}B\) of some group \(B\), then the group algebras \(LA\) and \(LB\) are isomorphic for some algebraically closed field \(L\). Under certain assumptions on \(R\) and \(A\) the authors also prove that \(R_tA\cong R_{t_1}B\) if and only if \(A\cong B\) and the factor set \(t_1\) is symmetric.