Components and realizability of fusion systems

2025/04/28 by Ellen Henke, Justin Lynd, Henke, Ellen +1
Mathematics · #20D05 #20D20 #20D35 #20E25 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2504.19826

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For p∈\2,3\ it is known that a saturated p-fusion system is realizable if and only if each of its components is realizable by a finite simple group. For primes p≥ 5 this is false. Building on work of Broto, Møller, Oliver and Ruiz, we show however that a fusion system F is realizable if and only if for each of its components C there exists a realizable subnormal subsystem E of F with O^{p^′}(E)=C.

Related

• Control of Fusion and Solubility in Fusion Systems
• Realizability and tameness of fusion systems
• Nonrealizability of certain representations in fusion systems
• Realizing fusion systems inside finite groups
• Uniqueness of factorization for fusion-invariant representations