Mathematics Subject Classification 1991

20-XX Group theory and generalizations ( 0 Dok.)

• 20-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 20-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 20-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 20-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 20-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 20-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 20Axx Foundations ( 0 Dok. )
• 20A05 Axiomatics and elementary properties ( 0 Dok.)
• 20A10 Metamathematical considerations, {For word problems, See 20F10} ( 0 Dok.)
• 20A15 Applications of logic to group theory ( 0 Dok.)
• 20A99 None of the above but in this section ( 0 Dok.)
• 20Bxx Permutation groups ( 0 Dok. )
• 20B05 General theory for finite groups ( 0 Dok.)
• 20B07 General theory for infinite groups ( 0 Dok.)
• 20B10 Characterization theorems ( 0 Dok.)
• 20B15 Primitive groups ( 0 Dok.)
• 20B20 Multiply transitive finite groups ( 0 Dok.)
• 20B22 Multiply transitive infinite groups ( 0 Dok.)
• 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures, See also {05Bxx, 12F10,20G40, 20H30, 51-XX} ( 0 Dok.)
• 20B27 Infinite automorphism groups, See also {12F10} ( 0 Dok.)
• 20B30 Symmetric groups ( 0 Dok.)
• 20B35 Subgroups of symmetric groups ( 0 Dok.)
• 20B40 Computational methods ( 0 Dok.)
• 20B99 None of the above but in this section ( 0 Dok.)
• 20Cxx Representation theory of groups, See also {19A22 (for representation rings and Burnside rings)} ( 0 Dok. )
• 20C05 Group rings of finite groups and their modules, See Also { 16S34} ( 0 Dok.)
• 20C07 Group rings of infinite groups and their modules, See Also { 16S34} ( 0 Dok.)
• 20C10 Integral representations of finite groups ( 0 Dok.)
• 20C11 $p$-adic representations of finite groups ( 0 Dok.)
• 20C12 Integral representations of infinite groups ( 0 Dok.)
• 20C15 Ordinary representations and characters ( 0 Dok.)
• 20C20 Modular representations and characters ( 0 Dok.)
• 20C25 Projective representations and multipliers ( 0 Dok.)
• 20C30 Representations of finite symmetric groups ( 0 Dok.)
• 20C32 Representations of infinite symmetric groups ( 0 Dok.)
• 20C33 Representations of finite groups of Lie type ( 0 Dok.)
• 20C34 Representations of sporadic groups ( 0 Dok.)
• 20C35 Applications of group representations to physics ( 0 Dok.)
• 20C40 Computational methods ( 0 Dok.)
• 20C99 None of the above but in this section ( 0 Dok.)
• 20Dxx Abstract finite groups ( 0 Dok. )
• 20D05 Classification of simple and nonsolvable groups ( 0 Dok.)
• 20D06 Simple groups: alternating groups and groups of Lie type, See also {20Gxx, 22Exx} ( 0 Dok.)
• 20D08 Simple groups: sporadic groups ( 0 Dok.)
• 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks, See also {20F17} ( 0 Dok.)
• 20D15 Nilpotent groups, $p$-groups ( 0 Dok.)
• 20D20 Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure ( 0 Dok.)
• 20D25 Special subgroups (Frattini, Fitting, etc.) ( 0 Dok.)
• 20D30 Series and lattices of subgroups ( 0 Dok.)
• 20D35 Subnormal subgroups ( 0 Dok.)
• 20D40 Products of subgroups ( 0 Dok.)
• 20D45 Automorphisms ( 0 Dok.)
• 20D50 Covering of subgroups ( 0 Dok.)
• 20D60 Arithmetic and combinatorial problems ( 0 Dok.)
• 20D99 None of the above but in this section ( 0 Dok.)
• 20Exx Structure and classification of infinite or finite groups ( 0 Dok. )
• 20E05 Free nonabelian groups ( 0 Dok.)
• 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations ( 0 Dok.)
• 20E07 Subgroup theorems ( 0 Dok.)
• 20E08 Groups acting on trees ( 0 Dok.)
• 20E10 Quasivarieties and varieties of groups ( 0 Dok.)
• 20E15 Chains and lattices of subgroups, subnormal subgroups, See also {20F22} ( 0 Dok.)
• 20E18 Limits, profinite groups ( 0 Dok.)
• 20E22 Extensions, wreath products, and other compositions, See also {20J05} ( 0 Dok.)
• 20E25 Local properties ( 0 Dok.)
• 20E26 Residual properties and generalizations ( 0 Dok.)
• 20E28 Maximal subgroups ( 0 Dok.)
• 20E32 Simple groups, See also {20D05} ( 0 Dok.)
• 20E34 General structure theorems ( 0 Dok.)
• 20E36 General theorems concerning automorphisms of groups ( 0 Dok.)
• 20E42 Groups with a $BN$-pair; buildings, See also {51E24} ( 0 Dok.)
• 20E99 None of the above but in this section ( 0 Dok.)
• 20Fxx Special aspects of infinite or finite groups ( 0 Dok. )
• 20F05 Generators, relations, and presentations ( 0 Dok.)
• 20F06 Cancellation theory; application of van Kampen diagrams, See also {57M05} ( 0 Dok.)
• 20F10 Word problems, other decision problems, connections with logic and automata, See also {03B25, 03D05, 03D40,06B25, 08A50, 68Qxx} ( 0 Dok.)
• 20F12 Commutator calculus ( 0 Dok.)
• 20F14 Derived series, central series, and generalizations ( 0 Dok.)
• 20F16 Solvable groups, supersolvable groups ( 0 Dok.)
• 20F17 Formations of groups, Fitting classes, See also {20D10} ( 0 Dok.)
• 20F18 Nilpotent groups ( 0 Dok.)
• 20F19 Generalizations of solvable and nilpotent groups ( 0 Dok.)
• 20F22 Other classes of groups defined by subgroup chains ( 0 Dok.)
• 20F24 FC-groups and their generalizations ( 0 Dok.)
• 20F28 Automorphism groups of groups, See also {20E36} ( 0 Dok.)
• 20F29 Representations of groups as automorphism groups of algebraic systems ( 0 Dok.)
• 20F32 Geometric group theory, See also {05C25, 20Exx, 20Gxx} ( 0 Dok.)
• 20F34 Fundamental groups and their automorphisms, See Also {57M05, 57Sxx, 22E40} ( 0 Dok.)
• 20F36 Braid groups; Artin groups ( 0 Dok.)
• 20F38 Other groups related to topology or analysis ( 0 Dok.)
• 20F40 Associated Lie structures ( 0 Dok.)
• 20F45 Engel conditions ( 0 Dok.)
• 20F50 Periodic groups; locally finite groups ( 0 Dok.)
• 20F55 Coxeter groups, See also {22E40} ( 0 Dok.)
• 20F60 Ordered groups See mainly{ 06F15} ( 0 Dok.)
• 20F99 None of the above but in this section ( 0 Dok.)
• 20Gxx Linear algebraic groups (classical groups), {For arithmetic theory, See 11E57, 11H06; for geometric theory, See 14Lxx, 22Exx; for other methods in representation theory, See { 15AQ30, 22Exx} { 15A30, 22E45, 22E46, 22E47, 22E50, 22E55}} ( 0 Dok. )
• 20G05 Representation theory ( 0 Dok.)
• 20G10 Cohomology theory ( 0 Dok.)
• 20G15 Linear algebraic groups over arbitrary fields ( 0 Dok.)
• 20G20 Linear algebraic groups over the reals, the complexes, the quaternions ( 0 Dok.)
• 20G25 Linear algebraic groups over local fields and their integers ( 0 Dok.)
• 20G30 Linear algebraic groups over global fields and their integers ( 0 Dok.)
• 20G35 Linear algebraic groups over adeles and other rings and schemes ( 0 Dok.)
• 20G40 Linear algebraic groups over finite fields ( 0 Dok.)
• 20G45 Applications to physics; explicit representations ( 0 Dok.)
• 20G99 None of the above but in this section ( 0 Dok.)
• 20Hxx Other groups of matrices, See also {15A30} ( 0 Dok. )
• 20H05 Unimodular groups, congruence subgroups, See also {11F06, 19B37, 22E40, 51F20} ( 0 Dok.)
• 20H10 Fuchsian groups and their generalizations, See also {11F06, 22E40, 30F35, 32Nxx} ( 0 Dok.)
• 20H15 Other geometric groups, including crystallographic groups, See also {51-XX, especially 51F15, and 82D25} ( 0 Dok.)
• 20H20 Other matrix groups over fields ( 0 Dok.)
• 20H25 Other matrix groups over rings ( 0 Dok.)
• 20H30 Other matrix groups over finite fields ( 0 Dok.)
• 20H99 None of the above but in this section ( 0 Dok.)
• 20Jxx Connections with homological algebra and category theory ( 0 Dok. )
• 20J05 Homological methods in group theory ( 0 Dok.)
• 20J06 Cohomology of finite groups ( 0 Dok.)
• 20J10 Groups arising as cohomology groups ( 0 Dok.)
• 20J15 Category of groups ( 0 Dok.)
• 20J99 None of the above but in this section ( 0 Dok.)
• 20Kxx Abelian groups ( 0 Dok. )
• 20K01 Finite abelian groups ( 0 Dok.)
• 20K05 Finitely generated groups ( 0 Dok.)
• 20K10 Torsion groups, primary groups and generalized primary groups ( 0 Dok.)
• 20K12 Ulm sequences ( 0 Dok.)
• 20K15 Torsion free groups, finite rank ( 0 Dok.)
• 20K20 Torsion free groups, infinite rank ( 0 Dok.)
• 20K21 Mixed groups ( 0 Dok.)
• 20K25 Direct sums, direct products, etc. ( 0 Dok.)
• 20K26 Indecomposable groups ( 0 Dok.)
• 20K27 Subgroups ( 0 Dok.)
• 20K30 Automorphisms, homomorphisms, endomorphisms, etc. ( 0 Dok.)
• 20K35 Extensions ( 0 Dok.)
• 20K40 Homological and categorical methods ( 0 Dok.)
• 20K45 Topological methods, See also {22A05, 22B05} ( 0 Dok.)
• 20K99 None of the above but in this section ( 0 Dok.)
• 20Lxx 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} ( 0 Dok. )
• 20L05 General theory ( 0 Dok.)
• 20L10 Connections with group theory ( 0 Dok.)
• 20L13 Mappings of groupoids ( 0 Dok.)
• 20L15 Connections with topology ( 0 Dok.)
• 20L17 Connections with category theory ( 0 Dok.)
• 20L99 None of the above but in this section ( 0 Dok.)
• 20Mxx Semigroups ( 0 Dok. )
• 20M05 Free semigroups, generators and relations, word problems ( 0 Dok.)
• 20M07 Varieties of semigroups ( 0 Dok.)
• 20M10 General structure theory ( 0 Dok.)
• 20M11 Radical theory ( 0 Dok.)
• 20M12 Ideal theory ( 0 Dok.)
• 20M14 Commutative semigroups ( 0 Dok.)
• 20M15 Mappings of semigroups ( 0 Dok.)
• 20M17 Regular semigroups ( 0 Dok.)
• 20M18 Inverse semigroups ( 0 Dok.)
• 20M19 Orthodox semigroups ( 0 Dok.)
• 20M20 Semigroups of transformations, etc., See also {47D03, 47H20, 54H15} ( 0 Dok.)
• 20M25 Semigroup rings, multiplicative semigroups of rings, See also {16S36, 16Y60} ( 0 Dok.)
• 20M30 Representation of semigroups ( 0 Dok.)
• 20M35 Semigroups in automata theory, linguistics, etc., See Also {03D05, 68Qxx, 68S05} ( 0 Dok.)
• 20M50 Connections of semigroups with homological algebra and category theory ( 0 Dok.)
• 20M99 None of the above but in this section ( 0 Dok.)
• 20Nxx Other generalizations of groups ( 0 Dok. )
• 20N02 Sets with a single binary operation (groupoids) ( 0 Dok.)
• 20N05 Loops, quasigroups, See also {05Bxx} ( 0 Dok.)
• 20N07 Mappings of loops ( 0 Dok.)
• 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.) ( 0 Dok.)
• 20N15 $n$-ary systems ( 0 Dok.)
• 20N20 Hypergroups ( 0 Dok.)
• 20N25 Fuzzy groups, See also {04A72} ( 0 Dok.)
• 20N99 None of the above but in this section ( 0 Dok.)
• 20P05 Probabilistic methods in group theory ( 0 Dok.)