On the Vertices of Indecomposable Modules Over Dihedral 2-Groups

Guodong Zhou

paper

On the Vertices of Indecomposable Modules Over Dihedral 2-Groups

arXiv:0709.0136

Abstract

Let $k$ be an algebraically closed field of characteristic 2. We compute the vertices of all indecomposable $k D_{8}$ -modules for the dihedral group $D_{8}$ of order 8. We also give a conjectural formula of the induced module of a string module from $k T_{0}$ to $k G$ where $G$ is a dihedral group of order $\geq 8$ and where $T_{0}$ is a dihedral subgroup of index 2 of $G$ . Some cases where we verified this formula are given.

19 pages