Proving a conjecture for fusion systems on a class of groups

2023/02/10 by Patrick Serwene, Serwene, Patrick
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2302.05203

openalex publication_date 2023/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove the conjecture that exotic and block-exotic fusion systems coincide holds for all fusion systems on exceptional p-groups of maximal nilpotency class, where p ≥ 5. This is done by considering a family of exotic fusion systems discovered by Parker and Stroth. Together with a previous result by the author, which we also generalise in this paper, and a result by Grazian and Parker this implies the conjecture for fusion systems on such groups. Considering small primes, there are no exotic fusion systems on 2-groups of maximal class and for p = 3, we prove block-exoticity of two exotic fusion systems described by Diaz--Ruiz--Viruel.

Related

• Block-Exoticity of a Family of Exotic Fusion Systems
• Exotic Fusion System on a Subgroup of the Monster
• Block fusion systems over maximal nilpotency class 3-groups
• Weight conjectures for fusion systems on an extraspecial group
• Fusion systems over a Sylow p-subgroup of G₂(p)