Fusion systems with Benson–Solomon components

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • Ellen Henke - , Chair of Mathematics (Author)
  • Justin Lynd - , University of Louisiana at Lafayette (Author)

Abstract

The Benson–Solomon systems comprise an infinite ascending family of simple exotic fusion systems at the prime 2. The results we prove give significant additional evidence that these are the only simple exotic 2-fusion systems, as conjectured by Solomon. We consider a saturated fusion system F having an involution centralizer with a component C isomorphic to a Benson–Solomon fusion system, and we show under rather general hypotheses that F cannot be simple. Furthermore, we prove that if F is almost simple with these properties, then F is isomorphic to the next larger Benson–Solomon system extended by a group of field automorphisms. Our results are situated within Aschbacher’s program to provide a new proof of a major part of the classification of finite simple groups via fusion systems. One of the most important steps in this program is a proof of Walter’s Theorem for fusion systems, and our first result is specifically tailored for use in the proof of that step. We then apply Walter’s Theorem to treat the general Benson–Solomon component problem under the assumption that each component of an involution centralizer in F is on the list of currently known quasisimple 2-fusion systems.

Details

Original languageEnglish
Pages (from-to)673–737
Number of pages65
JournalDuke Mathematical Journal
Volume171
Issue number3
Publication statusPublished - 15 Feb 2022
Peer-reviewedYes

External IDs

Scopus 85126325151

Keywords

Library keywords