La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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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.
• 20-99 Group theory and generalizations (not classified at a more specific level)
• 20Axx Foundations
• 20Bxx Permutation groups
• 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
• 20Dxx Abstract finite groups
• 20Exx Structure and classification of infinite or finite groups
• 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, 20M05, 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 20D15]
  • 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 groups, Coxeter groups [See also 22E40, 51F15]
  • 20F60 Ordered groups [See mainly 06F15]
  • 20F65 Geometric group theory [See also 05C25, 20E08, 57Mxx] [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 20F32
  • 20F67 Hyperbolic groups, nonpositively curved groups [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 20F32
  • 20F69 Asymptotic properties of groups [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 20F32
  • 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]
• 20Hxx Other groups of matrices [See also 15A30]
• 20Jxx Connections with homological algebra and category theory
• 20Kxx Abelian groups
• 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
• 20Nxx Other generalizations of groups
• 20P05 Probabilistic methods in group theory [See also 60Bxx]

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