20Bxx Permutation groups
This subtopic studies permutation groups, focusing on group actions, transitivity, primitive groups, and symmetry in combinatorial settings.
Specific topics
20B05 General theory for finite groups
Overview
20B05 studies general theory for finite groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general theory for finite groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B07 General theory for infinite groups
Overview
20B07 studies general theory for infinite groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general theory for infinite groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B10 Characterization theorems for permutation groups
Overview
20B10 studies characterization theorems for permutation groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for characterization theorems for permutation groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B15 Primitive groups
Overview
20B15 studies primitive groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for primitive groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B20 Multiply transitive finite groups
Overview
20B20 studies multiply transitive finite groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for multiply transitive finite groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B22 Multiply transitive infinite groups
Overview
20B22 studies multiply transitive infinite groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for multiply transitive infinite groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B25 Automorphism groups of algebraic, geometric, or combinatorial structures
Overview
20B25 studies automorphism groups of algebraic, geometric, or combinatorial structures in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for automorphism groups of algebraic, geometric, or combinatorial structures
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B27 Infinite automorphism groups
Overview
20B27 studies infinite automorphism groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for infinite automorphism groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B30 Symmetric groups
Overview
20B30 studies symmetric groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for symmetric groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B35 Subgroups of symmetric groups
Overview
20B35 studies subgroups of symmetric groups in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for subgroups of symmetric groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks
20B40 Computational methods (permutation groups)
Overview
20B40 studies computational methods (permutation groups) in permutation groups. It studies group actions on finite or infinite sets, with emphasis on transitivity, primitivity, and computational structure.
Related Wikipedia Page
Permutation Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for computational methods (permutation groups)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, algebraic algorithms, and the classification of symmetry actions.
Applications
- Group actions on sets
- Transitivity and primitivity
- Computational permutation-group methods
References
Recommended Textbooks