Group theory and generalizations Infinite groups and combinatorial group theory Concept
Presentation of a group
Summary
A presentation describes a group by a set of generators and a set of relations. The group is the quotient of the free group on by the normal subgroup generated by .
Where this leads
21 pages build on this one.
- Graph of groups
- Nichols algebra
- Conjugacy problem
- Artin group
- Coxeter group
- Right-angled Artin group
- Magnus's Freiheitssatz
- Random group
- Dehn function
- Finitely presented group
- Group isomorphism problem
- Andrews–Curtis conjecture
- Wirtinger presentation
- Higman embedding theorem
- Word problem for groups
- Small cancellation theory
- One-relator group
- Hopf's formula
- Braid group
- HNN extension
- Tietze transformations
Further reading
About this page
| Tag | 0JGEQXQ4AC |
|---|---|
| URI | m2://0JGEQXQ4AC |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20F05 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Graph of groups
- Conjugacy problem
- Artin group
- Coxeter group
- Right-angled Artin group
- Magnus's Freiheitssatz
- Random group
- Dehn function
- Finitely presented group
- Group isomorphism problem
- Andrews–Curtis conjecture
- Wirtinger presentation
- Higman embedding theorem
- Word problem for groups
- Small cancellation theory
- One-relator group
- Hopf's formula
- Braid group
- HNN extension
- Tietze transformations