Finite groups of OTP projective representation type

Volume 126 / 2012

Leonid F. Barannyk Colloquium Mathematicum 126 (2012), 35-51 MSC: Primary 16G60; Secondary 20C20, 20C25. DOI: 10.4064/cm126-1-2

Abstract

Let $K$ be a field of characteristic $p>0$, $K^*$ the multiplicative group of $K$ and $G=G_p\times B$ a finite group, where $G_p$ is a $p$-group and $B$ is a $p'$-group. Denote by $K^\lambda G$ a twisted group algebra of $G$ over $K$ with a $2$-cocycle $\lambda \in Z^2(G,K^*)$. We give necessary and sufficient conditions for $G$ to be of OTP projective $K$-representation type, in the sense that there exists a cocycle $\lambda \in Z^2(G,K^*)$ such that every indecomposable $K^\lambda G$-module is isomorphic to the outer tensor product $V\mathbin {\#} W$ of an indecomposable $K^\lambda G_p$-module $V$ and a simple $K^\lambda B$-module $W$. We also exhibit finite groups $G=G_p\times B$ such that, for any $\lambda \in Z^2(G,K^*)$, every indecomposable $K^\lambda G$-module satisfies this condition.

Authors

  • Leonid F. BarannykInstitute of Mathematics
    Pomeranian University of Słupsk
    Arciszewskiego 22b
    76-200 Słupsk, Poland
    e-mail

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