20-XX 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
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 {For representation rings and Burnside rings, see also 19A22}
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
20Dxx Abstract finite groups
20D05 Classification of simple and nonsolvable groups
20D06 Simple groups: alternating groups and groups of Lie type [See also 20Gxx, 22Exx]
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
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]
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
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]
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 20D10]
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
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}
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 ad\`eles 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
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
20H99 None of the above, but in this section
20Jxx 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
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}
20Mxx 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
20Nxx 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
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]