Quaternion Fusion Packets
About this Title
Michael Aschbacher, California Institute of Technology, Pasadena, CA
Publication: Contemporary Mathematics
Publication Year: 2021; Volume 765
ISBNs: 978-1-4704-5665-8 (print); 978-1-4704-6421-9 (online)
Let $p$ be a prime and $S$ a finite $p$-group. A $p$-fusion system on $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory.
The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
Graduate students and research mathematicians interested in the theory of finite groups.
Table of Contents
- Michael Aschbacher – Quanternion Fusion Packets