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05B Combinatorics: Designs and configurations

05C Combinatorics: Graph theory

05C05 Trees
05C10 Planar graphs; geometric and topological aspects of graph theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C76 Graph operations (line graphs, products, etc.)
05C81 Random walks on graphs

05E Combinatorics: Algebraic combinatorics

06A Order, lattices, ordered algebraic structures: Ordered sets

11M Number theory: Zeta and L-functions: analytic theory

11P Number theory: Additive number theory; partitions

11R Number theory: Algebraic number theory: global fields

14G Algebraic geometry: Arithmetic problems. Diophantine geometry

15A Linear and multilinear algebra; matrix theory: Basic linear algebra

15B Linear and multilinear algebra; matrix theory: Special matrices

16A Associative rings and algebras: Associative rings and algebras

16R Associative rings and algebras: Rings with polynomial identity

16S Associative rings and algebras: Rings and algebras arising under various constructions

16U Associative rings and algebras: Conditions on elements

17A Nonassociative rings and algebras: General nonassociative rings

17B Nonassociative rings and algebras: Lie algebras and Lie superalgebras

20A Group theory and generalizations: Foundations

20B Group theory and generalizations: Permutation groups

20B05 General theory for finite groups
20B07 General theory for infinite groups
20B10 Characterization theorems
20B15 Primitive groups
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
20B27 Infinite automorphism groups
20B30 Symmetric groups
20B35 Subgroups of symmetric groups

20C Group theory and generalizations: Representation theory of groups

20C05 Group rings of finite groups and their modules
20C07 Group rings of infinite groups and their modules
20C08 Hecke algebras and their representations
20C10 Integral representations of finite groups
20C15 Ordinary representations and characters
20C30 Representations of finite symmetric groups
20C40 Computational methods
20C99 None of the above, but in this section

20D Group theory and generalizations: Abstract finite groups

20D05 Finite simple groups and their classification
20D06 Simple groups: alternating groups and groups of Lie type
20D08 Simple groups: sporadic groups
20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
20D15 Nilpotent groups, p-groups
20D20 Sylow subgroups, Sylow properties, π-groups, π-structure
20D25 Special subgroups (Frattini, Fitting, etc.)
20D40 Products of subgroups
20D45 Automorphisms
20D50 Covering of subgroups
20D60 Arithmetic and combinatorial problems
20D99 None of the above, but in this section

20E Group theory and generalizations: Structure and classification of infinite or finite groups

20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E07 Subgroup theorems; subgroup growth
20E08 Groups acting on trees
20E10 Quasivarieties and varieties of groups
20E15 Chains and lattices of subgroups, subnormal subgroups
20E18 Limits, profinite groups
20E22 Extensions, wreath products, and other compositions
20E25 Local properties
20E26 Residual properties and generalizations; residually finite groups
20E32 Simple groups
20E34 General structure theorems
20E36 Automorphisms of infinite groups
20E45 Conjugacy classes
20E99 None of the above, but in this section

20F Group theory and generalizations: Special aspects of infinite or finite groups

20F05 Generators, relations, and presentations
20F10 Word problems, other decision problems, connections with logic and automata
20F12 Commutator calculus
20F14 Derived series, central series, and generalizations
20F15 Structure theorems
20F16 Solvable groups, supersolvable groups
20F17 Formations of groups, Fitting classes
20F18 Nilpotent groups
20F19 Generalizations of solvable and nilpotent groups
20F20 Limits, profinite groups
20F22 Other classes of groups defined by subgroup chains
20F24 FC-groups and their generalizations
20F28 Automorphism groups of groups
20F29 Representations of groups as automorphism groups of algebraic systems
20F36 Braid groups; Artin groups
20F40 Associated Lie structures
20F45 Engel conditions
20F50 Periodic groups; locally finite groups
20F55 Reflection and Coxeter groups
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
20F69 Asymptotic properties of groups
20F70 Algebraic geometry over groups; equations over groups
20F99 None of the above, but in this section

20G Group theory and generalizations: Linear algebraic groups and related topics

20 Group theory and generalizations

20H Group theory and generalizations: Other groups of matrices

20J Group theory and generalizations: Connections with homological algebra and category theory

20K Group theory and generalizations: Abelian groups

20M Group theory and generalizations: Semigroups

20N Group theory and generalizations: Other generalizations of groups

20P Group theory and generalizations: Probabilistic methods in group theory

22B Topological groups, Lie groups: Locally compact abelian groups (LCA groups)

37A Dynamical systems and ergodic theory: Ergodic theory

37B Dynamical systems and ergodic theory: Topological dynamics

43A Abstract harmonic analysis: Abstract harmonic analysis

60J Probability theory and stochastic processes: Markov processes

68Q Computer science: Theory of computing

94A Information and communication, circuits: Communication, information

94B Information and communication, circuits: Theory of error-correcting codes and error-detecting codes

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