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.

Key Words:

• Modular representation
• Outer tensor product
• Projective representation
• Twisted group algebra

2010 Mathematics Subject Classification:

• Primary 16G60
• Secondary 20C20, 20C25

Notes

Communicated by A. Smoktunowicz.