Control of fusion and solubility in fusion systems

Journal article

In this article, we consider control of fusion, quotients, and p-soluble fusion systems. For control of fusion, we prove the three main theorems in the literature in a new, largely elementary way, significantly shortening their proofs. To prove one of these, and a theorem of Aschbacher that the product of strongly closed subgroups is strongly closed, we produce a consolidated treatment of quotients, collating and expanding the constructions previously available; we include analogues of the isomorphism theorems for fusion systems. We move on to 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 it for more general fusion systems.

Authors: Craven, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Algebra
• Volume: 323
• Issue: 9
• Pages: 2429-2448
• Publication date: 2010-05-01
• Edition: Publisher's version
• DOI: 10.1016/j.jalgebra.2010.02.025
• ISSN: 0021-8693
• Language: English
• Keywords: p-soluble groups; control of fusion; fusion system
• Subjects: Group theory and generalizations (mathematics); Mathematics