Generalized 2-cocycles of finite groups and maximal orders

Abstract

Let R be a Dedekind domain with quotient field K and let G be a finite group. Let alpha: G x G --> R \ {0} be a generalized 2-cocycle, i.e., not necessarily taking its values in the units of R, and consider the generalized twisted group ring R *(alpha) G. In this paper we derive criteria for R *(alpha) G to be a graded maximal R-order, resp. a hereditary R-order or a maximal R-order(in K *(alpha) G). (C) 1998 Academic Press.