Subgroup families controlling p-local finite groups

DOI10.1112/S0024611505015327zbMath1090.20026arXivmath/0403042OpenAlexW2114448696MaRDI QIDQ5696023

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

Publication date: 7 October 2005

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

Full work available at URL: https://arxiv.org/abs/math/0403042

zbMATH Keywords

finite $p$-groups fusion categories fusion systems radical groups classifying spaces of groups $p$-local groups maps between classifying spaces linking categories

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Series and lattices of subgroups (20D30) Modular representations and characters (20C20) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Category of groups (20J15)

Related Items (66)

Fusion systems over non-resistant $\mathcal{A}_2$-groups ⋮ Saturated fusion systems over $\mathcal {A}_2$-groups ⋮ Reduced fusion systems over 2-groups of sectional rank at most 4 ⋮ Automorphisms of $p$-local compact groups ⋮ Normalizers of chains of discrete $p$-toral subgroups in compact Lie groups ⋮ Some products in fusion systems and localities ⋮ Cohomology with twisted coefficients of the classifying space of a fusion system ⋮ Extensions of linking systems with $p$-group kernel ⋮ Fusion systems over a Sylow $p$-subgroup of $\mathrm{G}_2(p)$ ⋮ The normaliser decomposition for $p$-local finite groups ⋮ Higher limits over the fusion orbit category ⋮ Centralizers of normal subsystems revisited ⋮ Minami-Webb splittings and some exotic $p$-local finite groups ⋮ Fusion systems and localities. ⋮ On $p$-stability in groups and fusion systems ⋮ Kernels of localities ⋮ Green correspondence on centric Mackey functors over fusion systems ⋮ Subgroup collections controlling the homotopy type of a $p$-local compact group ⋮ Vector bundles over classifying spaces of p‐local finite groups and Benson–Carlson duality ⋮ Saturated fusion systems with parabolic families. ⋮ $ZJ$-theorems for fusion systems ⋮ Punctured groups for exotic fusion systems ⋮ Analogues of Goldschmidt's thesis for fusion systems. ⋮ Normalizers of sets of components in fusion systems ⋮ Unstable Adams operations on $p$-local compact groups ⋮ Unstable Adams operations acting on $p$-local compact groups and fixed points ⋮ N-groups and fusion systems. ⋮ Group models for fusion systems ⋮ Reductions to simple fusion systems ⋮ Minimal fusion systems with a unique maximal parabolic. ⋮ An algebraic model for finite loop spaces ⋮ The gluing problem in the fusion systems of the symmetric, alternating and linear groups. ⋮ Amalgams, blocks, weights, fusion systems and finite simple groups. ⋮ Nilpotent fusion systems ⋮ On Thompson's $p$-complement theorems for saturated fusion systems. ⋮ Subcentric linking systems ⋮ Simplicity of fusion systems of finite simple groups ⋮ Sparse fusion systems ⋮ Splitting fusion systems over 2-groups ⋮ Realisability of $p$-stable fusion systems ⋮ Nilpotent $p$-local finite groups. ⋮ Generation of fusion systems of characteristic 2-type. ⋮ Minimal characteristic bisets for fusion systems ⋮ Homotopy equivalences between $p$-subgroup categories ⋮ Existence and uniqueness of classifying spaces for fusion systems over discretep-toral groups ⋮ A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver. ⋮ Control of fusion and solubility in fusion systems ⋮ Two families of exotic fusion systems. ⋮ Control of transfer and weak closure 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 ⋮ Glauberman’s and Thompson’s theorems for fusion systems ⋮ Recognizing SL2(q) in fusion systems ⋮ The Brauer indecomposability of Scott modules for the quadratic group $\mathrm{Qd}(p)$ ⋮ 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 ⋮ Reduction (mod $q$) of fusion system amalgams ⋮ Wreath products and representations of $p$-local finite groups. ⋮ Minimal Non-nilpotent and Locally Nilpotent Fusion Systems ⋮ Fusion systems ⋮ Saturated fusion systems over $2$-groups ⋮ Weight conjectures for fusion systems ⋮ Fusion systems and localities -- a dictionary ⋮ Extensions of $p$-local finite groups ⋮ Extensions of homomorphisms between localities

This page was built for publication: Subgroup families controlling p-local finite groups