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]
|