Finite groups of OTP projective representation type

Leonid F. Barannyk

Colloquium Mathematicae, Tome 126 (2012), p. 35-51 / Harvested from The Polish Digital Mathematics Library

Résumé

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 ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such 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 a simple $K^{λ}B$-module W. We also exhibit finite groups $G = G_{p} × B$ such that, for any λ ∈ Z²(G,K*), every indecomposable $K^{λ}G$-module satisfies this condition.

Détail

Publié le : 2012-01-01

Zbl 1242.16024

EUDML-ID : urn:eudml:doc:283789