| 20-XX | | Prev: 19 | Up: Top | Next: 22 | |
| 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 (must also be assigned at least one classification number from Section 01)
| 20-04 |
Explicit machine computation and programs (not the theory of computation or programming)
| 20-06 |
Proceedings, conferences, collections, etc.
| |
20Axx
| Foundations
[xref: 18B40]
| 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
| |
20Bxx |
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
| |
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]
[xref: 16S34]
| 20C07 |
Group rings of infinite groups and their modules [See also 16S34]
[xref: 16S34]
| 20C08 |
Hecke algebras and their representations
| 20C10 |
Integral representations of finite groups
[xref: 11R33]
| 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
[xref: 05E10]
| 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
[xref: 81R05]
| 20C40 |
Computational methods
| 20C99 |
None of the above, but in this section
| |
20Dxx |
Abstract finite groups
| 20D05 |
Classification of simple and nonsolvable groups
[xref: 20E32]
| 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]
[xref: 20F16, 20F17]
| 20D15 |
Nilpotent groups, $p$-groups
[xref: 20F18]
| 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
| |
20Exx |
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]
[xref: 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
[xref: 20F28]
| 20E42 |
Groups with a $BN$-pair; buildings [See also 51E24]
| 20E45 |
Conjugacy classes
| 20E99 |
None of the above, but in this section
| |
20Fxx |
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]
[xref: 03B25, 03D40, 06B25, 08A50]
| 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]
[xref: 20D10]
| 20F18 |
Nilpotent groups [See also 20D15]
| 20F19 |
Generalizations of solvable and nilpotent groups
| 20F22 |
Other classes of groups defined by subgroup chains
[xref: 20E15]
| 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]
[xref: 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]
[xref: 06F15]
| 20F65 |
Geometric group theory [See also 05C25, 20E08,57Mxx]
[xref: 05C25, 20E08]
| 20F67 |
Hyperbolic groups and nonpositively curved groups
| 20F69 |
Asymptotic properties of groups
| 20F99 |
None of the above, but in this section
| |
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}
[xref: 11E57, 14L35, 17B45, 20D06, 51N30]
| 20G05 |
Representation theory
[xref: 22E50, 22E55]
| 20G10 |
Cohomology theory
[xref: 11E72]
| 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
[xref: 20B25]
| 20G42 |
Quantum groups (quantized function algebras) and their representations [See also 16W35, 17B37, 81R50]
[xref: 16W35, 17B37]
| 20G45 |
Applications to physics
| 20G99 |
None of the above, but in this section
| |
20Hxx |
Other groups of matrices [See also 15A30]
[xref: 22E40]
| 20H05 |
Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]
[xref: 11F06, 19B37, 51F20, 51F25]
| 20H10 |
Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
[xref: 11F06, 30F35, 30F40, 32Nxx, 51F15]
| 20H15 |
Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]
[xref: 51F15]
| 20H20 |
Other matrix groups over fields
| 20H25 |
Other matrix groups over rings
| 20H30 |
Other matrix groups over finite fields
[xref: 20B25]
| 20H99 |
None of the above, but in this section
| |
20Jxx |
Connections with homological algebra and category theory
[xref: 18Gxx]
| 20J05 |
Homological methods in group theory
[xref: 20E22]
| 20J06 |
Cohomology of groups
| 20J15 |
Category of groups
| 20J99 |
None of the above, but in this section
| |
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
| 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}
[xref: 18B40]
| |
20Mxx |
Semigroups
[xref: 06F05, 18B40]
| 20M05 |
Free semigroups, generators and relations, word problems
| 20M07 |
Varieties of semigroups
| 20M10 |
General structure theory
[xref: 06A12]
| 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]
[xref: 54H15]
| 20M25 |
Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]
[xref: 16S36]
| 20M30 |
Representation of semigroups; actions of semigroups on sets
| 20M35 |
Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]
[xref: 68Q70, 94A45]
| 20M50 |
Connections of semigroups with homological algebra and category theory
| 20M99 |
None of the above, but in this section
| |
20Nxx |
Other generalizations of groups
| 20N02 |
Sets with a single binary operation (groupoids)
| 20N05 |
Loops, quasigroups [See also 05Bxx]
[xref: 51A25, 53A60]
| 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]
| |