On the definition of saturated fusion systems

DOI10.1515/JGT.2009.003zbMath1234.20028OpenAlexW1990998417MaRDI QIDQ3184185

Kieran Roberts, Sergey V. Shpectorov

Publication date: 13 October 2009

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

Full work available at URL: https://doi.org/10.1515/jgt.2009.003

zbMATH Keywords

conjugacy classes of subgroupssaturated fusion systemsfully normalized subgroupsfully centralized subgroupsreceptive subgroupssaturated subgroups

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

Saturated fusion systems over \(\mathcal {A}_2\)-groups, Brauer indecomposability of Scott modules, Kernels of localities, Saturated fusion systems over a class of finite \(p\)-groups., Relative stable equivalences of Morita type for the principal blocks of finite groups and relative Brauer indecomposability, Normalizers of sets of components in fusion systems, Transfer and characteristic idempotents for saturated fusion systems, Saturated fusion systems as idempotents in the double Burnside ring., Reductions to simple fusion systems, An algebraic model for finite loop spaces, On saturated fusion systems and Brauer indecomposability of Scott modules., Fusion systems for profinite groups, Minimal characteristic bisets for fusion systems, The rank of fusion systems, Fusion systems, Fusion systems on \(p\)-groups of sectional rank 3, The fibered Burnside group of a fusion system

Cites Work

• A reduction theorem for fusion systems of blocks.
• Simple fusion systems and the Solomon 2-local groups.
• Frobenius categories.
• The homotopy theory of fusion systems