Biblioteca Dr. Antonio Monteiro · Catálogo | |
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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