Mathematical subject classification for group theory

The Mathematical Subject Classification (MSC) is a classification scheme used for writings in mathematics. The scheme is used by the Americal Mathematical Society, as well as Zentralblatt Math. This article gives information on those aspects of the classification that are relevant for group theory.

General information about the classification=

The MSC works as follows. Every article is assigned a primary classification which gives that class to which it belongs the most. Apart from this, each article may also have some secondary classification numbers, which are other classes to which it can be said to belong. These are also called its cross-references.

The classification number has three parts. The first part is a number of one or two digits, which gives the overall head within which it lies. The second part is a letter of the alphabet, which stands for a second-level classification. The third part is again a one or two-digit number, which stands for a third-level classification.

There are two main headings:

• 20: For group theory and generalizations
• 22: For topological groups, Lie groups

Group theory and generalizations

List of writing types

• 00: General reference works
• 01: Instructional exposition
• 02: Research exposition (monograph, survey articles)
• 03: Historical
• 04: Explicit machine computations and programs
• 06: Proceedings, conferences and collections

Thus, something like 20-02 means a research exposition related to group theory.

List of subtopics

• A: Foundations
• B: Permutation group theory
• C: Group representation theory
• D: Finite group theory
• E: Structure and classification of infinite or finite groups
• F: Special aspects of infinite or finite groups
• G: Linear algebraic groups (classical groups)
• H: Other groups of matrices
• J: Connections with homological algebra and category theory
• K: Abelian group theory
• L05: Groupoids (small category where every morphism is an isomorphism)
• M: Semigroup theory
• N: Other generalizations of groups
• P05: Probabilistic methods in group theory

D: Finite group theory

20D is concerned with abstract finite groups, including classification problems as well as the subgroup theory of finite groups. Third-level headings within 20D:

• 20D05: Classification of simple and non-solvable groups
• 20D06: Simple groups: alternating groups and groups of Lie type
• 20D08: Simple groups: Sporadic groups
• 20D10: Solvable groups, theory of formations, Schunk classes, Fitting classes, $\pi$-length, and rank
• 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
• 20D69: None of the above, but in this section