Editing Geometric group theory (section)

== Examples ==

The following examples are often studied in geometric group theory:
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* [[Amenable group]]s
* [[Burnside group|Free Burnside groups]]
* The infinite [[cyclic group]] '''[[integer|Z]]'''
* [[Free group]]s
* [[Free product]]s
* [[Outer automorphism group]]s [[Out(Fn)|Out(F<sub>''n''</sub>)]] (via [[Outer space (group theory)|outer space]])
* [[Hyperbolic group]]s
* [[Mapping class group]]s (automorphisms of surfaces)
* [[Symmetric group]]s
* [[Braid group]]s
* [[Coxeter group]]s
* General [[Artin group]]s
* [[Thompson groups|Thompson's group]] ''F''
* [[CAT(0) group]]s
* [[Arithmetic group]]s
* [[Automatic group]]s 
* [[Fuchsian group]]s, [[Kleinian group]]s, and other groups acting properly discontinuously on symmetric spaces, in particular [[Lattice (discrete subgroup)|lattices]] in semisimple Lie groups.
* [[Wallpaper group]]s
* [[Baumslag–Solitar group]]s
* [[Graph of groups|Fundamental groups of graphs of groups]]
* [[Grigorchuk group]]
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