Indecomposable Projective Representations of Direct Products of Finite Groups Over a Field of Characteristic p

Abstract

Let K be a field of characteristic p > 0, K* the multiplicative group of K and G = G p × B a finite group, where G p is a p-group and B is a p′-group. Denote by K λ G a twisted group algebra of G over K with a 2-cocycle λ ∈Z 2(G, K*). In this article, we give necessary and sufficient conditions for K λ G to be of OTP representation type, in the sense that every indecomposable K λ G-module is isomorphic to the outer tensor product V#W of an indecomposable K λ G p -module V and an irreducible K λ B-module W.