On Thompson's \(p\)-complement theorems for saturated fusion systems.

DOI10.1215/21562261-3089100zbMath1332.20015arXiv1304.5352OpenAlexW3104514501MaRDI QIDQ500829

Albert Ruiz, Jon González-Sánchez, Antonio Viruel

Publication date: 5 October 2015

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.5352

zbMATH Keywords

Frobenius kernelsfixed-point-free automorphismssaturated fusion systems\(p\)-nilpotency criteriaThompson \(p\)-complement theorems

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15) Products of subgroups of abstract finite groups (20D40)

Related Items (1)

A cohomological characterization of nilpotent fusion systems

Cites Work

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• A characteristic subgroup for fusion systems.
• The classification of \(p\)-local finite groups over the extraspecial group of order \(p^3\) and exponent \(p\).
• Nilpotent \(p\)-local finite groups.
• Tate's and Yoshida's theorems on control of transfer for fusion systems
• FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER
• $ZJ$-theorems for fusion systems
• Glauberman’s and Thompson’s theorems for fusion systems
• The homotopy theory of fusion systems
• Equivalences of classifying spaces completed at odd primes
• Subgroup families controlling p-local finite groups
• Normal \(p\)-complements for finite groups
• Normal \(p\)-complements for finite groups

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