Endotrivial modules for finite groups schemes II
Group Theory
2011-04-04 v1
Abstract
It is well known that if G is a finite group then the group of endotrivial modules is finitely generated. In this paper we prove that for an arbitrary finite group scheme G, and for any fixed integer n > 0, there are only finitely many isomorphism classes of endotrivial modules of dimension n. This provides evidence to support the speculation that the group of endotrivial modules for a finite group scheme is always finitely generated. The result also has some applications to questions about lifting and twisting the structure of endotrivial modules in the case that G is an infinitesimal group scheme associated to an algebraic group.
Keywords
Cite
@article{arxiv.1104.0226,
title = {Endotrivial modules for finite groups schemes II},
author = {Jon F. Carlson and Daniel K. Nakano},
journal= {arXiv preprint arXiv:1104.0226},
year = {2011}
}