Recognizing SL2(q) in fusion systems

DOI10.1515/JGT.2010.017zbMath1252.20017MaRDI QIDQ3060804

Ellen Henke

Publication date: 10 December 2010

Published in: Journal of Group Theory (Search for Journal in Brave)

zbMATH Keywords

saturated fusion systemsessential subgroups\(\mathrm{SL}_2(q)\)minimal parabolic groups

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Special subgroups (Frattini, Fitting, etc.) (20D25) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Finite simple groups and their classification (20D05)

Related Items

Radical 3-subgroups of the finite groups of Lie type \(E_{6}\), Radical 3-subgroups of \(F_4(q)\) with \(q\) even., Uniqueness of factorization for fusion-invariant representations, Radical subgroups of the finite exceptional groups of Lie type \(E_6\)., The essential 2-rank of general linear and unitary groups, The essential rank of classical groups., Minimal fusion systems with a unique maximal parabolic., The AWC-goodness and essential rank of sporadic simple groups., Fusion systems containing pearls, Fusion systems, Fusion systems on a Sylow \(p\)-subgroup of \(G_2(p^n)\) or \(PSU_4(p^n)\)

Cites Work

• The \(P!\)-theorem
• The local \(C(G,T)\) theorem.
• Sylow intersections and fusion
• A conjugation family for finite groups
• Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt fest läßt
• Normal subsystems of fusion systems
• Glauberman’s and Thompson’s theorems for fusion systems
• 𝐹-stability in finite groups
• The homotopy theory of fusion systems
• Subgroup families controlling p-local finite groups