Examples
The following examples are often studied in geometric group theory:
- Amenable groups
- Free Burnside groups
- The infinite cyclic group Z
- Free groups
- Free products
- Outer automorphism groups Out(Fn) (via Outer space)
- Hyperbolic groups
- Mapping class groups (automorphisms of surfaces)
- Symmetric groups
- Braid groups
- Coxeter groups
- General Artin groups
- Thompson's group F
- CAT(0) groups
- Arithmetic groups
- Automatic groups
- Kleinian groups, and other lattices acting on symmetric spaces.
- Wallpaper groups
- Baumslag-Solitar groups
- Fundamental groups of graphs of groups
- Grigorchuk group
Read more about this topic: Geometric Group Theory
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