Normal Subsystems of Fusion Systems
Group Theory
2014-02-26 v1 Representation Theory
Abstract
In this article we prove that for any saturated fusion system, that the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether one uses weakly normal or normal subsystems. We also develop a theory of weakly normal maps, consider intersections and products of weakly normal subsystems, and the hypercentre of a fusion system.
Keywords
Cite
@article{arxiv.1006.2728,
title = {Normal Subsystems of Fusion Systems},
author = {David A. ~Craven},
journal= {arXiv preprint arXiv:1006.2728},
year = {2014}
}