Fusion systems on small 𝑝-groups

DOI10.1090/S0002-9947-2012-05580-2zbMath1286.20015arXiv1007.1639MaRDI QIDQ2844736

Adam Glesser, David A. Craven

Publication date: 19 August 2013

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

Full work available at URL: https://arxiv.org/abs/1007.1639

zbMATH Keywords

finite \(p\)-groupsautomorphismsmetacyclic \(p\)-groupssaturated fusion systemsresistant groups

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Special subgroups (Frattini, Fitting, etc.) (20D25) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Saturated fusion systems over \(\mathcal {A}_2\)-groups ⋮ On the Character Degrees of Suzukip-Groups of TypeAandC ⋮ The Brauer indecomposability of Scott modules with vertex $Q_{2^n}\times C_{2^m}$ ⋮ Groups with 2-generated Sylow subgroups and their character tables ⋮ A generalization of Alperin fusion theorem and its applications ⋮ Fusion Systems on Bicyclic 2-Groups ⋮ On finite \(p\)-groups of supersoluble type ⋮ Some remarks on subgroups, epimorphic images and p′-automorphisms of finite p-groups ⋮ The Brauer indecomposability of Scott modules with wreathed 2-group vertices ⋮ Splendid Morita equivalences for principal blocks with semidihedral defect groups ⋮ Donovan's conjecture and extensions by the centralizer of a defect group ⋮ Splendid Morita equivalences for principal 2-blocks with dihedral defect groups ⋮ Fusion systems ⋮ Fusion systems on a Sylow 3-subgroup of the McLaughlin group ⋮ Brauer indecomposability of Scott modules with semidihedral vertex

Cites Work

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• Fusion systems on metacyclic 2-groups.
• The gluing problem for some block fusion systems.
• Control of fusion and solubility in fusion systems
• A note on blocks with dihedral defect groups.
• On \(H^*(\mathcal C;k^\times)\) for fusion systems.
• On 2-groups of small rank admitting an automorphism of prime order \(p>3\)
• On 2-groups of small rank admitting an automorphism of order 3
• Suzuki 2-groups
• The Dade group of a metacyclic \(p\)-group
• Extensions of nilpotent blocks
• Fusion category algebras.
• On finite groups with dihedral Sylow 2-subgroups
• Central elements in core-free groups
• A classification of finite 2-groups with exactly three involutions.
• All 𝑝-local finite groups of rank two for odd prime 𝑝
• CONTROL OF FUSION IN FUSION SYSTEMS
• Extensions of $p$-local finite groups
• $ZJ$-theorems for fusion systems
• Normal subsystems of fusion systems
• The Dade group of a fusion system
• The homotopy theory of fusion systems
• Normal subsystems of fusion systems
• On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2
• On 2-Groups With No Normal Abelian Subgroups of Rank 3, and Their Occurrence as Sylow 2-Subgroups of Finite Simple Groups
• Endliche Gruppen I
• Finite Groups with Quasi-Dihedral and Wreathed Sylow 2-Subgroups
• On the Automorphism Group of A 2-Group