Realizing a fusion system by a single finite group.

DOI10.1007/s00013-010-0119-zzbMath1243.20025OpenAlexW2159470814MaRDI QIDQ974650

Sejong Park

Publication date: 4 June 2010

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10379/3730

zbMATH Keywords

\(p\)-subgroupsSylow subgroupsexotic fusion systemssaturated fusion systemsexoticity index

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Modular representations and characters (20C20) Frobenius induction, Burnside and representation rings (19A22)

Related Items (11)

A spectral sequence for fusion systems ⋮ Weights in a Benson-Solomon block ⋮ Fusion systems and constructing free actions on products of spheres ⋮ A theorem of Mislin for cohomology of fusion systems and applications to block algebras of finite groups ⋮ Representation rings for fusion systems and dimension functions ⋮ Minimal characteristic bisets and finite groups realizing Ruiz-Viruel exotic fusion systems. ⋮ Fusion systems and group actions with abelian isotropy subgroups ⋮ On cohomology of saturated fusion systems and support varieties. ⋮ Minimal characteristic bisets for fusion systems ⋮ The Brauer indecomposability of Scott modules for the quadratic group \(\mathrm{Qd}(p)\) ⋮ Realizing fusion systems inside finite groups

Cites Work

• Realising fusion systems.
• Saturated fusion systems as idempotents in the double Burnside ring.
• Frobenius categories versus Brauer blocks. The Grothendieck group of the Frobenius category of a Brauer block.
• Amalgams, blocks, weights, fusion systems and finite simple groups.
• The homotopy theory of fusion systems

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