20Fxx Infinite groups and combinatorial group theory
This subtopic studies infinite groups and combinatorial group theory, emphasizing presentations, generators and relations, and geometric or algorithmic methods.
Specific topics
20F05 Generators, relations, and presentations of groups
Overview
20F05 studies generators, relations, and presentations of groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for generators, relations, and presentations of groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F06 Cancellation theory; partially commutative groups
Overview
20F06 studies cancellation theory; partially commutative groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for cancellation theory; partially commutative groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F10 Word problems, other decision problems, connections with logic
Overview
20F10 studies word problems, other decision problems, connections with logic in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for word problems, other decision problems, connections with logic
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F11 Groups of finite Morley rank
Overview
20F11 studies groups of finite morley rank in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for groups of finite morley rank
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F12 Commutator calculus
Overview
20F12 studies commutator calculus in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for commutator calculus
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F14 Derived series, central series, and generalizations
Overview
20F14 studies derived series, central series, and generalizations in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for derived series, central series, and generalizations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F16 Solvable groups, supersolvable groups
Overview
20F16 studies solvable groups, supersolvable groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for solvable groups, supersolvable groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F17 Polycyclic groups
Overview
20F17 studies polycyclic groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for polycyclic groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F18 Nilpotent groups
Overview
20F18 studies nilpotent groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for nilpotent groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F19 Generalizations of solvable and nilpotent groups
Overview
20F19 studies generalizations of solvable and nilpotent groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for generalizations of solvable and nilpotent groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F22 Other classes of groups defined by subgroup chains
Overview
20F22 studies other classes of groups defined by subgroup chains in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other classes of groups defined by subgroup chains
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F24 FC-groups and their generalizations
Overview
20F24 studies fc-groups and their generalizations in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fc-groups and their generalizations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F28 Automorphism groups of groups
Overview
20F28 studies automorphism groups of groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for automorphism groups of groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F29 Representations of groups as automorphism groups of algebraic systems
Overview
20F29 studies representations of groups as automorphism groups of algebraic systems in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of groups as automorphism groups of algebraic systems
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F34 Fundamental groups and their automorphisms
Overview
20F34 studies fundamental groups and their automorphisms in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fundamental groups and their automorphisms
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F36 Braid groups; Artin groups
Overview
20F36 studies braid groups; artin groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for braid groups; artin groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F38 Other groups related to topology or analysis
Overview
20F38 studies other groups related to topology or analysis in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other groups related to topology or analysis
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F40 Associated Lie structures for groups
Overview
20F40 studies associated lie structures for groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for associated lie structures for groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F45 Engel conditions
Overview
20F45 studies engel conditions in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for engel conditions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F50 Periodic groups; locally finite groups
Overview
20F50 studies periodic groups; locally finite groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for periodic groups; locally 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 to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F55 Reflection and Coxeter groups (group-theoretic aspects)
Overview
20F55 studies reflection and coxeter groups (group-theoretic aspects) in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for reflection and coxeter groups (group-theoretic aspects)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F60 Ordered groups
Overview
20F60 studies ordered groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for ordered groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F65 Geometric group theory
Overview
20F65 studies geometric group theory in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for geometric group theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F67 Hyperbolic groups and nonpositively curved groups
Overview
20F67 studies hyperbolic groups and nonpositively curved groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for hyperbolic groups and nonpositively curved groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F69 Asymptotic properties of groups
Overview
20F69 studies asymptotic properties of groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for asymptotic properties of groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks
20F70 Algebraic geometry over groups; equations over groups
Overview
20F70 studies algebraic geometry over groups; equations over groups in infinite groups and combinatorial group theory. It studies presentations, decision problems, and large-scale combinatorial structure of groups, especially infinite or geometric cases.
Related Wikipedia Page
Infinite Groups And Combinatorial Group Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for algebraic geometry over groups; equations over groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze word problems, subgroup growth, and geometric properties of groups.
Applications
- Presentations and decision problems
- Geometric group theory
- Combinatorial and computational methods
References
Recommended Textbooks