Control of Fusion and Solubility in Fusion Systems

Details Control of Fusion and Solubility in Fusion Systems Control of Fusion and Solubility in Fusion Systems

2009-10-05

arxiv.org/abs/0910.0725v1

Mathematics

Group Theory

24 pages

Scientific paper

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.

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