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05B Combinatorics: Designs and configurations
05B25 Finite geometries
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
05E05 Symmetric functions and generalizations
05E15 Combinatorial aspects of groups and algebras
06A Order, lattices, ordered algebraic structures: Ordered sets
06A15 Galois correspondences, closure operators
11M Number theory: Zeta and L-functions: analytic theory
11M41 Other Dirichlet series and zeta functions
11P Number theory: Additive number theory; partitions
11P83 Partitions; congruences and congruential restrictions
11R Number theory: Algebraic number theory: global fields
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
14G Algebraic geometry: Arithmetic problems. Diophantine geometry
14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
15A Linear and multilinear algebra; matrix theory: Basic linear algebra
15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
15A69 Multilinear algebra, tensor products
15B Linear and multilinear algebra; matrix theory: Special matrices
15B99 None of the above, but in this section
16A Associative rings and algebras: Associative rings and algebras
16A27 Group rings of infinite groups
16R Associative rings and algebras: Rings with polynomial identity
16R10 T-ideals, identities, varieties of rings and algebras
16S Associative rings and algebras: Rings and algebras arising under various constructions
16S34 Group rings, Laurent polynomial rings
16U Associative rings and algebras: Conditions on elements
16U60 Units, groups of units
17A Nonassociative rings and algebras: General nonassociative rings
17A01 General theory
17B Nonassociative rings and algebras: Lie algebras and Lie superalgebras
17B30 Solvable, nilpotent (super)algebras
17B56 Cohomology of Lie (super)algebras
20A Group theory and generalizations: Foundations
20A15 Applications of logic to group theory
20A99 None of the above, but in this section
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
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
20F99 None of the above, but in this section
20G Group theory and generalizations: Linear algebraic groups and related topics
20G05 Representation theory
20G25 Linear algebraic groups over local fields and their integers
20G35 Linear algebraic groups over adèles and other rings and schemes
20G40 Linear algebraic groups over finite fields
20 Group theory and generalizations
20-04 Explicit machine computation and programs
20H Group theory and generalizations: Other groups of matrices
20H20 Other matrix groups over fields
20H25 Other matrix groups over rings
20J Group theory and generalizations: Connections with homological algebra and category theory
20J05 Homological methods in group theory
20J06 Cohomology of groups
20J15 Category of groups
20K Group theory and generalizations: Abelian groups
20K01 Finite abelian groups
20K25 Direct sums, direct products, etc.
20K27 Subgroups
20K30 Automorphisms, homomorphisms, endomorphisms, etc.
20K35 Extensions
20M Group theory and generalizations: Semigroups
20M30 Representation of semigroups; actions of semigroups on sets
20N Group theory and generalizations: Other generalizations of groups
20N05 Loops, quasigroups
20P Group theory and generalizations: Probabilistic methods in group theory
20P05 Probabilistic methods in group theory
22B Topological groups, Lie groups: Locally compact abelian groups (LCA groups)
22B05 General properties and structure of LCA groups
37A Dynamical systems and ergodic theory: Ergodic theory
37A30 Ergodic theorems, spectral theory, Markov operators
37B Dynamical systems and ergodic theory: Topological dynamics
37B10 Symbolic dynamics
37B15 Cellular automata
43A Abstract harmonic analysis: Abstract harmonic analysis
43A20 L^1-algebras on groups, semigroups, etc.
43A62 Hypergroups
43A85 Analysis on homogeneous spaces
60J Probability theory and stochastic processes: Markov processes
60J10 Markov chains
68Q Computer science: Theory of computing
68Q80 Cellular automat
94A Information and communication, circuits: Communication, information
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
94B Information and communication, circuits: Theory of error-correcting codes and error-detecting codes
94B60 Other types of codes