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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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