Lower defect groups and vertices of simple modules
Representation Theory
2022-03-02 v1 Group Theory
Abstract
We compare lower defect groups associated with -regular classes and vertices of simple modules for a block of a finite group algebra. We show that lower defect groups are contained in vertices of simple modules after suitable reordering. Moreover, for a block of principal type, we show that a -regular lower defect group which contains a vertex of simple module is a defect group of the block.
Cite
@article{arxiv.2203.00313,
title = {Lower defect groups and vertices of simple modules},
author = {Akihiko Hida and Masao Kiyota},
journal= {arXiv preprint arXiv:2203.00313},
year = {2022}
}
Comments
10 pages