Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic
Volume 129 / 2012
Abstract
Let $S$ be a commutative complete discrete valuation domain of positive characteristic $p$, $S^*$ the unit group of $S$, $\varOmega $ a subgroup of $S^*$ and $G=G_p\times B$ a finite group, where $G_p$ is a $p$-group and $B$ is a $p'$-group. Denote by $S^\lambda G$ the twisted group algebra of $G$ over $S$ with a $2$-cocycle $\lambda \in Z^2(G,S^*)$. For $\varOmega $ satisfying a specific condition, we give necessary and sufficient conditions for $G$ to be of OTP projective $(S,\varOmega )$-representation type, in the sense that there exists a cocycle $\lambda \in Z^2(G,\varOmega )$ such that every indecomposable $S^\lambda G$-module is isomorphic to the outer tensor product $V\mathbin {\#} W$ of an indecomposable $S^\lambda G_p$-module $V$ and an irreducible $S^\lambda B$-module $W$.
