Sparse fusion systems

DOI10.1017/S0013091512000090zbMath1269.20013arXiv1005.5503OpenAlexW2963318699MaRDI QIDQ4911204

Adam Glesser

Publication date: 14 March 2013

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

Full work available at URL: https://arxiv.org/abs/1005.5503

zbMATH Keywords

finite \(p\)-groupsnilpotent blockssaturated fusion systemsThompson subgroup\(p\)-nilpotency criteriaextremely sparse fusion systems

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 nilpotent groups, (p)-groups (20D15)

Related Items (4)

Exponent and \(p\)-rank of finite \(p\)-groups and applications. ⋮ Nilpotent fusion systems ⋮ Nilpotent \(p\)-local finite groups. ⋮ Control of transfer and weak closure in fusion systems.

Cites Work

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• A characteristic subgroup of \(\Sigma_ 4\)-free groups
• Control of transfer and weak closure in fusion systems.
• The Solomon system \({\mathcal F}_{\text{Sol}}(3)\) does not occur as fusion system of a 2-block.
• Extensions of $p$-local finite groups
• $ZJ$-theorems for fusion systems
• The homotopy theory of fusion systems
• Subgroup families controlling p-local finite groups
• Focal Series in Finite Groups
• Normal \(p\)-complements for finite groups

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