FINITE GROUPS OF OTP PROJECTIVE REPRESENTATION TYPE OVER A COMPLETE DISCRETE VALUATION DOMAIN OF POSITIVE CHARACTERISTIC

Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Omega a subgroup of S* and G = G(p) x B a finite group, where G(p) is a p-group and B is a p'-group. Denote by S(lambda)G the twisted group algebra of G over S with a 2-cocycle lambda is an element of Z(2) (G, S*). For Omega satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S, Omega)-representation type, in the sense that there exists a cocycle lambda is an element of Z(2) (G, Omega) such that every indecomposable S(lambda)G-module is isomorphic to the outer tensor product V # W of an indecomposable S(lambda)G(p)-module V and an irreducible (SB)-B-lambda-module W.