Extensions of $p$-local finite groups

DOI10.1090/S0002-9947-07-04225-0zbMath1145.55013arXivmath/0502359OpenAlexW1972887940MaRDI QIDQ3433739

Carles Broto, Natàlia Castellana, Jesper Grodal, Ran Levi, Robert Oliver

Publication date: 2 May 2007

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

Full work available at URL: https://arxiv.org/abs/math/0502359

zbMATH Keywords

finite groupsclassifying spacefusion\(p\)-completion

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Homology of classifying spaces and characteristic classes in algebraic topology (55R40)

Related Items (53)

Fusion systems with Benson-Solomon components ⋮ On exotic saturated fusion systems. ⋮ Endotrivial modules for finite groups via homotopy theory ⋮ Strongly closed subgroups of finite groups. ⋮ Reduced fusion systems over 2-groups of sectional rank at most 4 ⋮ Cohomology with twisted coefficients of the classifying space of a fusion system ⋮ Extensions of linking systems with \(p\)-group kernel ⋮ Fusion systems and amalgams. ⋮ A completion theorem for fusion systems ⋮ A spectral sequence for fusion systems ⋮ Reduced fusion systems over 2-groups of small order ⋮ Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I. ⋮ Kernels of localities ⋮ On the composition product of saturated fusion systems. ⋮ Saturated fusion systems with parabolic families. ⋮ Realizability and tameness of fusion systems ⋮ Unstable Adams operations acting on \(p\)-local compact groups and fixed points ⋮ Transfer and characteristic idempotents for saturated fusion systems ⋮ On blocks of finite groups with central hyperfocal subgroups. ⋮ Resolutions, relation modules and Schur multipliers for categories ⋮ Fusion systems realizing certain Todd modules ⋮ Saturated fusion systems as idempotents in the double Burnside ring. ⋮ Reductions to simple fusion systems ⋮ An algebraic model for finite loop spaces ⋮ A ghost ring for the left-free double Burnside ring and an application to fusion systems ⋮ Nilpotent fusion systems ⋮ On the cohomology rings of small categories ⋮ Fusion systems on a Sylow \(p\)-subgroup of \(SU_4(p)\) ⋮ Subcentric linking systems ⋮ Simplicity of fusion systems of finite simple groups ⋮ Sparse fusion systems ⋮ Splitting fusion systems over 2-groups ⋮ A reduction theorem for fusion systems of blocks. ⋮ Nilpotent \(p\)-local finite groups. ⋮ A characterization of the 2-fusion system of \(L_4(q)\). ⋮ Control of fusion and solubility in fusion systems ⋮ Extensions of linking systems and fusion systems ⋮ On the homotopy type of the non-completed classifying space of a p-local finite group ⋮ Finite-dimensional algebras arising as blocks of finite group algebras ⋮ A characteristic subgroup for fusion systems. ⋮ The generalized Fitting subsystem of a fusion system ⋮ Automorphisms of fusion systems of finite simple groups of Lie typeandAutomorphisms of fusion systems of sporadic simple groups ⋮ Wreath products and representations of \(p\)-local finite groups. ⋮ Fusion systems ⋮ Saturated fusion systems over $2$-groups ⋮ Fusion systems on small 𝑝-groups ⋮ Equivalences between fusion systems of finite groups of Lie type ⋮ All 𝑝-local finite groups of rank two for odd prime 𝑝 ⋮ Fusion systems and localities -- a dictionary ⋮ Heilbronn characters ⋮ On the homotopy groups of \(p\)-completed classifying spaces ⋮ A cohomological characterization of nilpotent fusion systems ⋮ Extensions of homomorphisms between localities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homotopy classification of self-maps of \(BG\) via \(G\)-actions. II
• Homotopy equivalences of \(p\)-completed classifying spaces of finite groups
• The hyperfocal subalgebra of a block
• Towers of fibrations and homotopical wreath products
• Central elements in core-free groups
• Sylow intersections and fusion
• Homotopy limits, completions and localizations
• The homotopy theory of fusion systems
• Equivalences of classifying spaces completed at odd primes
• Cohomologies et extensions de catégories.
• Equivalences of classifying spaces completed at the prime two
• Subgroup families controlling p-local finite groups
• Simplicial homotopy theory

This page was built for publication: Extensions of $p$-local finite groups