Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

Leonid F. Barannyk ; Dariusz Klein

Colloquium Mathematicae, Tome 126 (2012), p. 173-187 / Harvested from The Polish Digital Mathematics Library

Résumé

Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and $G = G_{p} × B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $S^{λ}G$ the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable $S^{λ}G$-module is isomorphic to the outer tensor product V W of an indecomposable $S^{λ}G_{p}$-module V and an irreducible $S^{λ}B$-module W.

Détail

Publié le : 2012-01-01

Zbl 1273.16026

EUDML-ID : urn:eudml:doc:284058