# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

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

### Tom 129 / 2012

Colloquium Mathematicum 129 (2012), 173-187 MSC: Primary 16G60; Secondary 20C20, 20C25. DOI: 10.4064/cm129-2-2

#### Streszczenie

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 $W$.

#### Autorzy

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

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek