Group theory and generalizations Infinite groups and combinatorial group theory Concept
Free group
Summary
The free group on a set is the group of reduced words on , with concatenation followed by reduction as the operation. It is the group generated by with no relations other than those that the group axioms force.
Where this leads
32 pages build on this one.
- Out(F_n)
- Right-angled Artin group
- Kurosh problem
- Magnus's Freiheitssatz
- Stallings–Swan theorem
- Random group
- Margulis superrigidity theorem
- Banach–Tarski paradox
- Cohomological dimension of a group
- Lattice-ordered group
- Free probability
- Growth rate of a group
- Dehn function
- Finitely presented group
- Andrews–Curtis conjecture
- Word problem for groups
- Amenable group
- Small cancellation theory
- One-relator group
- Left-orderable group
- Tits alternative
- Kurosh subgroup theorem
- Hopf's formula
- Tietze transformations
- Universal property
- Torsion-free group
- Nielsen–Schreier theorem
- Schottky group
- Jordan–Schur theorem
- Burnside problem
- Grushko theorem
- Orderable group
Further reading
- Web https://en.wikipedia.org/wiki/Free_group, lead section
About this page
| Tag | 0KTW26C80J |
|---|---|
| URI | m2://0KTW26C80J |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20E05 |
| Specializes | Group |
| 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)
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What links here
Definitions
Used by
- Out(F_n)
- Right-angled Artin group
- Magnus's Freiheitssatz
- Stallings–Swan theorem
- Random group
- Margulis superrigidity theorem
- Cohomological dimension of a group
- Free probability
- Growth rate of a group
- Dehn function
- Finitely presented group
- Andrews–Curtis conjecture
- Word problem for groups
- Amenable group
- Small cancellation theory
- One-relator group
- Tits alternative
- Kurosh subgroup theorem
- Hopf's formula
- Tietze transformations
- Universal property
- Torsion-free group
- Nielsen–Schreier theorem
- Schottky group
- Jordan–Schur theorem
- Burnside problem
- Grushko theorem