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

Leonid F. Barannyk, and Dariusz Klein. "Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic." Colloquium Mathematicae 129.2 (2012): 173-187. <http://eudml.org/doc/284058>.

@article{LeonidF2012,
abstract = {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.},
author = {Leonid F. Barannyk, Dariusz Klein},
journal = {Colloquium Mathematicae},
keywords = {finite groups; indecomposable modules; twisted group algebras; outer tensor products; OTP representation type; projective representations; modular representations},
language = {eng},
number = {2},
pages = {173-187},
title = {Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic},
url = {http://eudml.org/doc/284058},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Leonid F. Barannyk
AU - Dariusz Klein
TI - Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 2
SP - 173
EP - 187
AB - 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.
LA - eng
KW - finite groups; indecomposable modules; twisted group algebras; outer tensor products; OTP representation type; projective representations; modular representations
UR - http://eudml.org/doc/284058
ER -