CONTROL OF FUSION IN FUSION SYSTEMS

DOI10.1142/S0219498806002034zbMath1118.20020MaRDI QIDQ3421573

Radu Stancu

Publication date: 7 February 2007

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

finite \(p\)-groupsfusion systemscontrol of fusionresistant groups\(p\)-local structures

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Modular representations and characters (20C20) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Finite nilpotent groups, (p)-groups (20D15) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Category of groups (20J15)

Related Items (29)

Fusion systems over non-resistant \(\mathcal{A}_2\)-groups ⋮ Remarks on chains of weakly closed subgroups ⋮ Saturated fusion systems over \(\mathcal {A}_2\)-groups ⋮ Cartan matrices and Brauer's \(k(B)\)-conjecture V ⋮ On the focal subgroup of a saturated fusion system ⋮ The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups ⋮ A note on Olsson's conjecture. ⋮ Saturated fusion systems over a class of finite \(p\)-groups. ⋮ Groups with 2-generated Sylow subgroups and their character tables ⋮ Saturated fusion systems with parabolic families. ⋮ A generalization of Alperin fusion theorem and its applications ⋮ Fusion systems on metacyclic 2-groups. ⋮ Fusion Systems on Bicyclic 2-Groups ⋮ On finite \(p\)-groups of supersoluble type ⋮ Blocks of full defect with nonabelian metacyclic defect groups. ⋮ Fusion systems for profinite groups ⋮ On Olsson's conjecture for blocks with metacyclic defect groups of odd order. ⋮ Control of fusion and solubility in fusion systems ⋮ On Brauer's \(k(B)\)-problem for blocks with metacyclic defect groups of odd order. ⋮ Glauberman’s and Thompson’s theorems for fusion systems ⋮ Donovan's conjecture and extensions by the centralizer of a defect group ⋮ The rank of fusion systems ⋮ A characteristic subgroup for fusion systems. ⋮ Minimal Non-nilpotent and Locally Nilpotent Fusion Systems ⋮ Fusion systems ⋮ Isotypies for \(p\)-blocks with non-abelian metacyclic defect groups, \(p\) odd ⋮ On the Number of Ordinary Irreducible Characters in ap-Block with a Minimal Nonabelian Defect Group ⋮ Fusion systems on small 𝑝-groups ⋮ 2-Fusion Systems with Components of Type SL₂(q)

Cites Work

• On group homomorphisms inducing mod-\(p\) cohomology isomorphisms
• Local methods in block theory
• The mod-p cohomology rings of metacyclic groups
• Stable splittings of classifying spaces of metacyclic \(p\)-groups, \(p\) odd
• \(p\)-nilpotence, classifying space indecomposability, and other properties of almost all finite groups
• On the cohomology and homotopy of Swan groups
• The Dade group of a metacyclic \(p\)-group
• Almost all generalized extraspecial \(p\)-groups are resistant
• Simple fusion systems and the Solomon 2-local groups.
• Almost all 𝑝-groups have automorphism group a 𝑝-group
• The homotopy theory of fusion systems
• Almost all extraspecial p-groups are swan groups

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