La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

Question : CC = Groups
05-XX Combinatorics [For finite fields, see 11Txx]

• 05C25 Graphs and groups [See also 20F65]
• 05E15 Combinatorial problems concerning the classical groups [See also 22E45, 33C80]
• 05E25 Group actions on posets and homology groups of posets [See also 06A11]

06-XX Order, lattices, ordered algebraic structures [See also 18B35]

• 06F05 Ordered semigroups and monoids [See also 20Mxx]
• 06F15 Ordered groups [See also 20F60]
• 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]

11-XX Number theory

• 11Exx Forms and linear algebraic groups [See also 19Gxx] [For quadratic forms in linear algebra, see 15A63]
• 11E57 Classical groups [See also 14Lxx, 20Gxx]
• 11E72 Galois cohomology of linear algebraic groups [See also 20G10]
• 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
• 11Fxx Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14-XX, 22Exx, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] [For relations with quadratic forms, see 11E45]
• 11F06 Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]
• 11F22 Relationship to Lie algebras and finite simple groups
• 11F41 Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
• 11F46 Siegel modular groups and their modular and automorphic forms
• 11F55 Other groups and their modular and automorphic forms (several variables)
• 11F75 Cohomology of arithmetic groups
• 11H56 Automorphism groups of lattices
• 11R29 Class numbers, class groups, discriminants
• 11R56 Adele rings and groups
• 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.) [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 11R58
• 11R65 Class groups and Picard groups of orders
• 11S31 Class field theory; p-adic formal groups [See also 14L05]

13-XX Commutative rings and algebras

• 13A50 Actions of groups on commutative rings; invariant theory [See also 14L24]
• 13C20 Class groups [See also 11R29]
• 13D15 Grothendieck groups, K-theory [See also 14C35, 18F25, 18F30, 19Axx, 19D50]

14-XX Algebraic geometry

• 14C15 Chow groups and rings
• 14C22 Picard groups
• 14F22 Brauer groups of schemes [See also 12G05, 16K50] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 13A20
• 14F35 Homotopy theory; fundamental groups [See also 14H30]
• 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 14D20, 14H30, 20E18
• 14Lxx Algebraic groups [For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45]
• 14L05 Formal groups, p-divisible groups [See also 55N22]
• 14L17 Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]
• 14L35 Classical groups (geometric aspects) [See also 20Gxx, 51N30]
• 14L40 Other algebraic groups (geometric aspects)

16-XX Associative rings and algebras [For the commutative case, see 13-XX]

• 16E20 Grothendieck groups, K-theory, etc. [See also 18F30, 19Axx, 19D50]
• 16K50 Brauer groups [See also 12G05, 14F22] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 13A20
• 16U60 Units, groups of units
• 16W22 Actions of groups and semigroups; invariant theory [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 16W20
• 16W35 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 16W30

17-XX Nonassociative rings and algebras

• 17Bxx Lie algebras and Lie superalgebras [For Lie groups, see 22Exx]
• 17B37 Quantum groups (quantized enveloping algebras) and related deformations [See also 16W35, 20G42, 81R50, 82B23]
• 17B45 Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
• 17C30 Associated groups, automorphisms

18-XX Category theory; homological algebra [For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology]

• 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]
• 18F30 Grothendieck groups [See also 13D15, 16E20, 19Axx]

19-XX $K$-theory [See also 16E20, 18F25]

• 19Axx Grothendieck groups and K₀ [See also 13D15, 18F30]
• 19Bxx Whitehead groups and K₁
• 19B14 Stability for linear groups
• 19Cxx Steinberg groups and K₂
• 19G12 Witt groups of rings [See also 11E81]

20-XX Group theory and generalizations

• 20Bxx Permutation groups
• 20B05 General theory for finite groups
• 20B07 General theory for infinite groups
• 20B15 Primitive groups
• 20B20 Multiply transitive finite groups
• 20B22 Multiply transitive infinite groups
• 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]
• 20B27 Infinite automorphism groups [See also 12F10]
• 20B30 Symmetric groups
• 20B35 Subgroups of symmetric groups
• 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
• 20C05 Group rings of finite groups and their modules [See also 16S34]
• 20C07 Group rings of infinite groups and their modules [See also 16S34]
• 20C10 Integral representations of finite groups
• 20C11 p-adic representations of finite groups
• 20C12 Integral representations of infinite groups
• 20C30 Representations of finite symmetric groups
• 20C32 Representations of infinite symmetric groups
• 20C33 Representations of finite groups of Lie type
• 20C34 Representations of sporadic groups
• 20Dxx Abstract finite groups
• 20D05 Classification of simple and nonsolvable groups
• 20D06 Simple groups: alternating groups and groups of Lie type [See also 20Gxx]
• 20D08 Simple groups: sporadic groups
• 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, -length, ranks [See also 20F17]
• 20D15 Nilpotent groups, p-groups
• 20D20 Sylow subgroups, Sylow properties, -groups, -structure
• 20D25 Special subgroups (Frattini, Fitting, etc.)
• 20D30 Series and lattices of subgroups
• 20D35 Subnormal subgroups
• 20D40 Products of subgroups
• 20Exx Structure and classification of infinite or finite groups
• 20E05 Free nonabelian groups
• 20E08 Groups acting on trees [See also 20F65]
• 20E10 Quasivarieties and varieties of groups
• 20E15 Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
• 20E18 Limits, profinite groups
• 20E28 Maximal subgroups
• 20E32 Simple groups [See also 20D05]
• 20E36 General theorems concerning automorphisms of groups
• 20E42 Groups with a BN-pair; buildings [See also 51E24]
• 20Fxx Special aspects of infinite or finite groups
• 20F16 Solvable groups, supersolvable groups [See also 20D10]
• 20F17 Formations of groups, Fitting classes [See also 20D10]
• 20F18 Nilpotent groups [See also 20D15]
• 20F19 Generalizations of solvable and nilpotent groups
• 20F22 Other classes of groups defined by subgroup chains
• 20F24 FC-groups and their generalizations
• 20F28 Automorphism groups of groups [See also 20E36]
• 20F29 Representations of groups as automorphism groups of algebraic systems
• 20F34 Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
• 20F36 Braid groups; Artin groups
• 20F38 Other groups related to topology or analysis
• 20F50 Periodic groups; locally finite groups
• 20F55 Reflection groups, Coxeter groups [See also 22E40, 51F15]
• 20F60 Ordered groups [See mainly 06F15]
• 20F67 Hyperbolic groups, nonpositively curved groups [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 20F32
• 20F69 Asymptotic properties of groups [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 20F32
• 20Gxx Linear algebraic groups (classical groups) [For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55]
• 20G15 Linear algebraic groups over arbitrary fields
• 20G20 Linear algebraic groups over the reals, the complexes, the quaternions
• 20G25 Linear algebraic groups over local fields and their integers
• 20G30 Linear algebraic groups over global fields and their integers
• 20G35 Linear algebraic groups over adèles and other rings and schemes
• 20G40 Linear algebraic groups over finite fields
• 20G42 Quantum groups (quantized function algebras) and their representations [See also 16W35, 17B37, 81R50] [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 16W30, 17B37
• 20Hxx Other groups of matrices [See also 15A30]
• 20H05 Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]
• 20H10 Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
• 20H15 Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]
• 20H20 Other matrix groups over fields
• 20H25 Other matrix groups over rings
• 20H30 Other matrix groups over finite fields
• 20J06 Cohomology of groups
• 20J15 Category of groups
• 20Kxx Abelian groups
• 20K01 Finite abelian groups
• 20K10 Torsion groups, primary groups and generalized primary groups
• 20K15 Torsion-free groups, finite rank
• 20K20 Torsion-free groups, infinite rank
• 20K21 Mixed groups
• 20K27 Subgroups
• 20Mxx Semigroups
• 20M05 Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10]
• 20M07 Varieties of semigroups
• 20M14 Commutative semigroups
• 20M15 Mappings of semigroups
• 20M17 Regular semigroups
• 20M18 Inverse semigroups
• 20M19 Orthodox semigroups
• 20M20 Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]
• 20M25 Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]
• 20M30 Representation of semigroups; actions of semigroups on sets
• 20M35 Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]
• 20M50 Connections of semigroups with homological algebra and category theory
• 20Nxx Other generalizations of groups
• 20N05 Loops, quasigroups [See also 05Bxx]
• 20N20 Hypergroups
• 20N25 Fuzzy groups [See also 03E72]

22-XX Topological groups, Lie groups [For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX]

• 22-99 Topological groups, Lie groups (not classified at a more specific level)
• 22A05 Structure of general topological groups
• 22A10 Analysis on general topological groups
• 22A15 Structure of topological semigroups
• 22A20 Analysis on topological semigroups
• 22A25 Representations of general topological groups and semigroups
• 22Bxx Locally compact abelian groups (LCA groups)
• 22B05 General properties and structure of LCA groups
• 22B10 Structure of group algebras of LCA groups
• 22C05 Compact groups
• 22Dxx Locally compact groups and their algebras
• 22D05 General properties and structure of locally compact groups
• 22D10 Unitary representations of locally compact groups
• 22D12 Other representations of locally compact groups
• 22D15 Group algebras of locally compact groups
• 22D40 Ergodic theory on groups [See also 28Dxx]
• 22D45 Automorphism groups of locally compact groups
• 22Exx Lie groups [For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90]
• 22E05 Local Lie groups [See also 34-XX, 35-XX, 58H05]
• 22E10 General properties and structure of complex Lie groups [See also 32M05]
• 22E15 General properties and structure of real Lie groups
• 22E20 General properties and structure of other Lie groups
• 22E25 Nilpotent and solvable Lie groups
• 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
• 22E30 Analysis on real and complex Lie groups [See also 33C80, 43-XX]
• 22E35 Analysis on p-adic Lie groups
• 22E40 Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
• 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods [For the purely algebraic theory, see 20G05]
• 22E46 Semisimple Lie groups and their representations
• 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
• 22E50 Representations of Lie and linear algebraic groups over local fields [See also 20G05]
• 22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings [See also 20G05]
• 22E60 Lie algebras of Lie groups [For the algebraic theory of Lie algebras, see 17Bxx]
• 22E65 Infinite-dimensional Lie groups and their Lie algebras [See also 17B65, 58B25, 58H05]
• 22E67 Loop groups and related constructions, group-theoretic treatment [See also 58D05]
• 22E70 Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]
• 22Fxx Noncompact transformation groups
• 22F30 Homogeneous spaces [For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups see especially 22E40] [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 57M60, 57Sxx, 22E40
• 22F50 Groups as automorphisms of other structures [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 22Axx, 46Lxx

28-XX Measure and integration [For analysis on manifolds, see 58-XX]

• 28C10 Set functions and measures on topological groups, Haar measures, invariant measures [See also 22Axx, 43A05]
• 28D15 General groups of measure-preserving transformations

30-XX Functions of a complex variable [For analysis on manifolds, see 58-XX]

• 30F35 Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
• 30F40 Kleinian groups [See also 20H10]

32-XX Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12]

• 32C35 Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]
• 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
• 32M17 Automorphism groups of Cⁿ and affine manifolds [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 32M05

33-XX Special functions (33-XX deals with the properties of functions as functions) [For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx]

• 33C80 Connections with groups and algebras, and related topics
• 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics

37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]

• 37A15 General groups of measure-preserving transformation [See mainly 22Fxx] [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 22D40, 28D15, 58F11
• 37F30 Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 30C99, 30F35, 30F40, 30F60, 58F23
• 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 58D05, 58D25, 58F05
• 37L05 General theory, nonlinear semigroups, evolution equations [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 34G20, 35Bxx, 35K22, 35L99, 47H20, 58D25, 58F39
• 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 34G20, 47H20, 58D25, 58F30, 58F39

43-XX Abstract harmonic analysis [For other analysis on topological and Lie groups, see 22Exx]

• 43A05 Measures on groups and semigroups, etc.
• 43A07 Means on groups, semigroups, etc.; amenable groups
• 43A10 Measure algebras on groups, semigroups, etc.
• 43A15 L^p-spaces and other function spaces on groups, semigroups, etc.
• 43A17 Analysis on ordered groups, H^p-theory
• 43A20 L¹-algebras on groups, semigroups, etc.
• 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
• 43A25 Fourier and Fourier-Stieltjes transforms on locally compact abelian groups
• 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 43A35 Positive definite functions on groups, semigroups, etc.
• 43A40 Character groups and dual objects
• 43A45 Spectral synthesis on groups, semigroups, etc.
• 43A55 Summability methods on groups, semigroups, etc. [See also 40J05]
• 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
• 43A62 Hypergroups
• 43A65 Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]
• 43A70 Analysis on specific locally compact abelian groups [See also 11R56, 22B05]
• 43A75 Analysis on specific compact groups
• 43A77 Analysis on general compact groups
• 43A80 Analysis on other specific Lie groups [See also 22Exx]

46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]

• 46L57 Derivations, dissipations and positive semigroups in C^*-algebras

47-XX Operator theory

• 47Dxx Groups and semigroups of linear operators, their generalizations and applications
• 47D03 Groups and semigroups of linear operators [For nonlinear operators, see 47H20; see also 20M20]
• 47D06 One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
• 47D07 Markov semigroups and applications to diffusion processes [For Markov processes, see 60Jxx]
• 47D08 Schrödinger and Feynman-Kac semigroups [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 35J10, 47D06, 47D07
• 47D60 C-semigroups [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 47D03, 47D06
• 47D62 Integrated semigroups [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 47D03, 47D06
• 47H20 Semigroups of nonlinear operators

51-XX Geometry [For algebraic geometry, see 14-XX]

• 51F15 Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]
• 51F25 Orthogonal and unitary groups [See also 20H05]
• 51Jxx Incidence groups
• 51J10 Projective incidence groups
• 51N25 Analytic geometry with other transformation groups
• 51N30 Geometry of classical groups [See also 20Gxx, 14L35]

54-XX General topology [For the topology of manifolds of all dimensions, see 57Nxx]

• 54H11 Topological groups [See also 22A05]
• 54H15 Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]

55-XX Algebraic topology

• 55M35 Finite groups of transformations (including Smith theory) [See also 57S17]
• 55Qxx Homotopy groups
• 55Q05 Homotopy groups, general; sets of homotopy classes
• 55Q07 Shape groups
• 55Q10 Stable homotopy groups
• 55Q20 Homotopy groups of wedges, joins, and simple spaces
• 55Q35 Operations in homotopy groups
• 55Q40 Homotopy groups of spheres
• 55Q52 Homotopy groups of special spaces
• 55Q55 Cohomotopy groups
• 55Q70 Homotopy groups of special types [See also 55N05, 55N07]
• 55Q91 Equivariant homotopy groups [See also 19L47]
• 55R35 Classifying spaces of groups and H-spaces

57-XX Manifolds and cell complexes [For complex manifolds, see 32Qxx]

• 57R67 Surgery obstructions, Wall groups [See also 19J25]
• 57Sxx Topological transformation groups [See also 20F34, 22-XX, 37-XX, 54H15, 58D05]
• 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
• 57S10 Compact groups of homeomorphisms
• 57S15 Compact Lie groups of differentiable transformations
• 57S17 Finite transformation groups
• 57S20 Noncompact Lie groups of transformations
• 57S25 Groups acting on specific manifolds
• 57S30 Discontinuous groups of transformations
• 57Txx Homology and homotopy of topological groups and related structures
• 57T10 Homology and cohomology of Lie groups
• 57T15 Homology and cohomology of homogeneous spaces of Lie groups
• 57T20 Homotopy groups of topological groups and homogeneous spaces

58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]

• 58B32 Geometry of quantum groups [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 58B30
• 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
• 58D07 Groups and semigroups of nonlinear operators [See also 17B65, 47H20]
• 58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
• 58H05 Pseudogroups and differentiable groupoids [See also 22A22, 22E65]

60-XX Probability theory and stochastic processes [For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX]

• 60B15 Probability measures on groups, Fourier transforms, factorization

81-XX Quantum theory

• 81Rxx Groups and algebras in quantum theory
• 81R05 Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]
• 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]
• 81R50 Quantum groups and related algebraic methods [See also 16W30, 17B37]

83-XX Relativity and gravitational theory

• 83C40 Gravitational energy and conservation laws; groups of motions

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