2009/10/05 by Craven, David A
#20C20 #20D20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.0910.0725
In this article, we consider the control of fusion in fusion systems, proving three previously known, non-trivial results in a new, largely elementary way. We then reprove a result of Aschbacher, that the product of two strongly closed subgroups is strongly closed; to do this, we consolidate the theory of quotients of fusion systems into a consistent theory. We move on considering p-soluble fusion systems, and prove that they are constrained, allowing us to effectively characterize fusion systems of p-soluble groups. This leads us to recast Thompson Factorization for Qd(p)-free fusion systems, and consider Thompson Factorization for more general fusion systems.