Local control in fusion systems of \(p\)-blocks of finite groups.

DOI10.1016/S0021-8693(02)00517-3zbMath1053.20007OpenAlexW2064096425MaRDI QIDQ1858258

Radha Kessar, Geoffrey R. Robinson, Markus Linckelmann

Publication date: 12 February 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-8693(02)00517-3

zbMATH Keywords

defect groupsBrauer categoriesGlauberman functorsAlperin-Goldschmidt conjugation

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Modular representations and characters (20C20) Quasi-Frobenius rings (16L60)

Related Items (19)

Fusion category algebras. ⋮ Weight conjectures for ordinary characters. ⋮ Cohomology algebras of 2-blocks of finite groups with defect groups of rank two. ⋮ Cohomology algebras of blocks of finite groups and Brauer correspondence. ⋮ Controlled 2-blocks of quasisimple groups ⋮ \textit{ZJ}-controlled blocks of quasisimple groups for odd primes ⋮ $ZJ$-theorems for fusion systems ⋮ On blocks of finite groups with central hyperfocal subgroups. ⋮ Amalgams, blocks, weights, fusion systems and finite simple groups. ⋮ Large character heights, \(Qd(p)\), and the ordinary weight conjecture. ⋮ Controlled blocks of the finite quasisimple groups for odd primes. ⋮ On the control of fusion in the local category for the \(p\)-block with a minimal nonabelian defect group. ⋮ Simple fusion systems and the Solomon 2-local groups. ⋮ The Solomon system \({\mathcal F}_{\text{Sol}}(3)\) does not occur as fusion system of a 2-block. ⋮ Cohomology algebras of blocks of finite groups and Brauer correspondence. II. ⋮ Real subpairs and Frobenius-Schur indicators of characters in 2-blocks. ⋮ A characteristic subgroup for fusion systems. ⋮ On the Number of Ordinary Irreducible Characters in ap-Block with a Minimal Nonabelian Defect Group ⋮ Extra special defect groups of order \(p^3\) and exponent \(p^2\).

Cites Work

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• Local methods in block theory
• Zur Darstellungstheorie der Gruppen endlicher Ordnung. I, II
• Brauer coefficients of p-subgroups associated with a p-block of a finite group
• Cancellation theorems related to conjectures of Alperin and Dade
• Extensions of nilpotent blocks
• A block theoretic analogue of a theorem of Glauberman and Thompson
• The homotopy theory of fusion systems
• A Characteristic Subgroup of a p-Stable Group
• Subgroups of finite groups
• On finite groups and their characters

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