Glauberman’s and Thompson’s theorems for fusion systems

DOI10.1090/S0002-9939-08-09690-1zbMath1163.20009MaRDI QIDQ3605000

Sejong Park, Nadia Mazza, Antonio Díaz Ramos, Adam Glesser

Publication date: 25 February 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

finite \(p\)-groupsThompson subgroupfusion systemsconjugation families\(p\)-nilpotency criteria

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Special subgroups (Frattini, Fitting, etc.) (20D25) Finite nilpotent groups, (p)-groups (20D15)

Related Items (10)

Centralizers of normal subsystems revisited ⋮ Analogues of Goldschmidt's thesis for fusion systems. ⋮ Minimal fusion systems with a unique maximal parabolic. ⋮ Nilpotent fusion systems ⋮ On Thompson's \(p\)-complement theorems for saturated fusion systems. ⋮ Nilpotent \(p\)-local finite groups. ⋮ Control of transfer and weak closure in fusion systems. ⋮ Recognizing SL2(q) in fusion systems ⋮ Minimal Non-nilpotent and Locally Nilpotent Fusion Systems ⋮ Fusion systems

Cites Work

• Unnamed Item
• Local methods in block theory
• Simple fusion systems and the Solomon 2-local groups.
• Frobenius categories.
• Sylow intersections and fusion
• Weakly closed elements of Sylow subgroups
• CONTROL OF FUSION IN FUSION SYSTEMS
• $ZJ$-theorems for fusion systems
• The homotopy theory of fusion systems
• Subgroup families controlling p-local finite groups
• Normal \(p\)-complements for finite groups

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