Fusion systems (Q2822846)

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scientific article; zbMATH DE number 6632862

Language	Label	Description	Also known as
English	Fusion systems	scientific article; zbMATH DE number 6632862

Statements

scholarly article

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Fusion systems (English)

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Michael Aschbacher

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publication date

5 October 2016

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zbMATH Keywords

fusion

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Sylow subgroups

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finite simple groups

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classifying spaces

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modular representation theory

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MaRDI profile type

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full work available at URL

https://doi.org/10.1090/bull/1538

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Sylow intersections and fusion

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Local methods in block theory

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Reduced, tame and exotic fusion systems

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Reduced fusion systems over 2-groups of small order

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A characterization of Chevalley groups over fields of odd order. I, II

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Normal subsystems of fusion systems

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The generalized Fitting subsystem of a fusion system

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Generation of fusion systems of characteristic 2-type.

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<i>S</i><sub>3</sub>-free 2-fusion systems

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Fusion systems of \(\mathbf F_2\)-type.

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N-groups and fusion systems.

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A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver.

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Group cohomology and control of \(p\)-fusion.

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Homotopy limits, completions and localizations

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Some applications of the theory of blocks of characters of finite groups. IV

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Subgroup families controlling p-local finite groups

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Extensions of $p$-local finite groups

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On spaces of self-homotopy equivalences of \(p\)-completed classifying spaces of finite groups and homotopy group extensions.

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Homotopy equivalences of \(p\)-completed classifying spaces of finite groups

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The homotopy theory of fusion systems

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Discrete models for the \(p\)-local homotopy theory of compact Lie groups and \(p\)-compact groups

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An algebraic model for finite loop spaces

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Equivalences between fusion systems of finite groups of Lie type

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Automorphisms of fusion systems of finite simple groups of Lie typeandAutomorphisms of fusion systems of sporadic simple groups

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A Frobenius theorem for blocks

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Fusion systems and localities.

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The linking systems of the Solomon 2-local finite groups are simply connected

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Two families of exotic fusion systems.

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Control of fusion and solubility in fusion systems

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Normal subsystems of fusion systems

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Fusion systems on small \(p\)-groups.

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Reduced fusion systems over \(p\)-groups with abelian subgroup of index \(p\). II

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Blocks with cyclic defect groups

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Glauberman’s and Thompson’s theorems for fusion systems

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Control of transfer and weak closure in fusion systems.

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All 𝑝-local finite groups of rank two for odd prime 𝑝

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Centric Maps and Realization of Diagrams in the Homotopy Category

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A New Finite Loop Space at the Prime Two

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Strongly closed subgroups of finite groups.

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A characterization of finite groups containing a strongly closed 2-subgroup

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Central elements in core-free groups

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A Characteristic Subgroup of a <i>p</i>-Stable Group

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Control of fixed points and existence and uniqueness of centric linking systems

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A conjugation family for finite groups

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2-fusion in finite groups

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Finite approximations of \(p\)-local compact groups

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Finite groups whose 2-subgroups are generated by at most 4 elements

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On the indecomposable representations of a finite group

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Recognizing SL2(q) in fusion systems

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Minimal fusion systems with a unique maximal parabolic.

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Products in fusion systems.

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A characterization of saturated fusion systems over Abelian 2-groups.

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Subcentric linking systems

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Unstable Adams operations on \(p\)-local compact groups

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The Solomon system \({\mathcal F}_{\text{Sol}}(3)\) does not occur as fusion system of a 2-block.

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$ZJ$-theorems for fusion systems

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A reduction theorem for fusion systems of blocks.

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Extensions of nilpotent blocks

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Existence and uniqueness of classifying spaces for fusion systems over discrete<i>p</i>-toral groups

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Correction to: Construction of 2-local finite groups of a type studied by Solomon and Benson

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Generalized Davis-Januszkiewicz spaces, multicomplexes and monomial rings

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The gluing problem does not follow from homological properties of \(\Delta_p(G)\).

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The gluing problem in the fusion systems of the symmetric, alternating and linear groups.

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Fusion category algebras.

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On \(H^*(\mathcal C;k^\times)\) for fusion systems.

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The Thompson-Lyons transfer lemma for fusion systems

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A characterization of the 2-fusion system of \(L_4(q)\).

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Unstable homotopy classification of

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Equivalences of classifying spaces completed at odd primes

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Equivalences of classifying spaces completed at the prime two

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Extensions of linking systems and fusion systems

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Existence and uniqueness of linking systems: Chermak's proof via obstruction theory

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Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I.

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Reduced fusion systems over 2-groups of sectional rank at most 4

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Reductions to simple fusion systems

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Extensions of linking systems with \(p\)-group kernel

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Saturated fusion systems over $2$-groups

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On 2-blocks with quaternion and quasihedral defect groups

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Saturated fusion systems with parabolic families.

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The gluing problem for some block fusion systems.

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A family of fusion systems related to the groups \(\mathrm{Sp}_4(p^a)\) and \(\mathrm G_2(p^a)\).

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Nilpotent blocks and their source algebras

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The hyperfocal subalgebra of a block

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Frobenius categories.

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Frobenius categories versus Brauer blocks. The Grothendieck group of the Frobenius category of a Brauer block.

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The spectrum of an equivariant cohomology ring. I. II

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Classifying spectra of saturated fusion systems

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Saturated fusion systems as idempotents in the double Burnside ring.

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On the definition of saturated fusion systems

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Exotic normal fusion subsystems of general linear groups

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The classification of \(p\)-local finite groups over the extraspecial group of order \(p^3\) and exponent \(p\).

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Fusion systems on metacyclic 2-groups.

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Classifying spaces and spectral sequences

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Finite groups with Sylow 2-subgroups of type .3

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CONTROL OF FUSION IN FUSION SYSTEMS

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Fusion systems for profinite groups

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Geometric topology. Localization, periodicity and Galois symmetry. The 1970 MIT Notes. Edited by A. Ranicki

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Nonsolvable finite groups all of whose local subgroups are solvable

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Saturated fusion systems over a class of finite \(p\)-groups.

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Bulletin of the American Mathematical Society. New Series

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1090/BULL/1538

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Sitelinks

Mathematics(1 entry)

mardi Publication:2822846

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