Baoyu Zhang (University of Birmingham) – Fusion systems and essential subgroups

Local finite group theory has been an important topic, particularly via the Classification of Finite Simple Groups. Fusion systems are categories defined on p-groups, which have helped simplify and extend much of the theory in the last 20 years and are starting to link group theory, representation theory, and algebraic topology. By Alperin-Goldschmidt's fusion theorem, a saturated fusion system can be completely determined by its essential subgroups. In this talk, I will discuss fusion systems with two-generator essential subgroups and present some other results on fusion systems.