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Navegando por la clasificación temática MSC 2000: 20 · Group theory and generalizations
20 Group theory and generalizations
  20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
  20-01 Instructional exposition (textbooks, tutorial papers, etc.)
  20-02 Research exposition (monographs, survey articles)
  20-03 Historical
  20-04 Explicit machine computation and programs (not the theory of computation or programming)
  20-06 Proceedings, conferences, collections, etc.
  20-99 Group theory and generalizations (not classified at a more specific level)
  20A Foundations
    20A05 Axiomatics and elementary properties
    20A10 Metamathematical considerations {For word problems, see 20F10}
    20A15 Applications of logic to group theory
    20A99 None of the above, but in this section
  20B Permutation groups
    20B05 General theory for finite groups
    20B07 General theory for infinite groups
    20B10 Characterization theorems
    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
    20B40 Computational methods
    20B99 None of the above, but in this section
  20C 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]
    20C08 Hecke algebras and their representations
    20C10 Integral representations of finite groups
    20C11 $p$-adic representations of finite groups
    20C12 Integral representations of infinite groups
    20C15 Ordinary representations and characters
    20C20 Modular representations and characters
    20C25 Projective representations and multipliers
    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
    20C35 Applications of group representations to physics
    20C40 Computational methods
    20C99 None of the above, but in this section
  20D 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, $\pi$-length, ranks [See also 20F17]
    20D15 Nilpotent groups, $p$-groups
    20D20 Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure
    20D25 Special subgroups (Frattini, Fitting, etc.)
    20D30 Series and lattices of subgroups
    20D35 Subnormal subgroups
    20D40 Products of subgroups
    20D45 Automorphisms
    20D60 Arithmetic and combinatorial problems
    20D99 None of the above, but in this section
  20E Structure and classification of infinite or finite groups
    20E05 Free nonabelian groups
    20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
    20E07 Subgroup theorems; subgroup growth
    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
    20E22 Extensions, wreath products, and other compositions [See also 20J05]
    20E25 Local properties
    20E26 Residual properties and generalizations
    20E28 Maximal subgroups
    20E32 Simple groups [See also 20D05]
    20E34 General structure theorems
    20E36 General theorems concerning automorphisms of groups
    20E42 Groups with a $BN$-pair; buildings [See also 51E24]
    20E45 Conjugacy classes
    20E99 None of the above, but in this section
  20F Special aspects of infinite or finite groups
    20F05 Generators, relations, and presentations
    20F06 Cancellation theory; application of van Kampen diagrams [See also 57M05]
    20F10 Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]
    20F12 Commutator calculus
    20F14 Derived series, central series, and generalizations
    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
    20F40 Associated Lie structures
    20F45 Engel conditions
    20F50 Periodic groups; locally finite groups
    20F55 Reflection and Coxeter groups [See also 22E40, 51F15]
    20F60 Ordered groups [See mainly 06F15]
    20F65 Geometric group theory [See also 05C25, 20E08, 57Mxx]
    20F67 Hyperbolic groups and nonpositively curved groups
    20F69 Asymptotic properties of groups
    20F99 None of the above, but in this section
  20G 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}
    20G05 Representation theory
    20G10 Cohomology theory
    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]
    20G45 Applications to physics
    20G99 None of the above, but in this section
  20H 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
    20H99 None of the above, but in this section
  20J Connections with homological algebra and category theory
    20J05 Homological methods in group theory
    20J06 Cohomology of groups
    20J15 Category of groups
    20J99 None of the above, but in this section
  20K 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
    20K25 Direct sums, direct products, etc.
    20K27 Subgroups
    20K30 Automorphisms, homomorphisms, endomorphisms, etc.
    20K35 Extensions
    20K40 Homological and categorical methods
    20K45 Topological methods [See also 22A05, 22B05]
    20K99 None of the above, but in this section
  20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05}
  20M Semigroups
    20M05 Free semigroups, generators and relations, word problems
    20M07 Varieties of semigroups
    20M10 General structure theory
    20M11 Radical theory
    20M12 Ideal theory
    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
    20M99 None of the above, but in this section
  20N Other generalizations of groups
    20N02 Sets with a single binary operation (groupoids)
    20N05 Loops, quasigroups [See also 05Bxx]
    20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
    20N15 $n$-ary systems $(n\ge 3)$
    20N20 Hypergroups
    20N25 Fuzzy groups [See also 03E72]
    20N99 None of the above, but in this section
  20P05 Probabilistic methods in group theory [See also 60Bxx]

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