Editing Cayley graph (section)

=== Geometric group theory ===
For infinite groups, the [[Coarse structure|coarse geometry]] of the Cayley graph is fundamental to [[geometric group theory]]. For a [[finitely generated group]], this is independent of choice of finite set of generators, hence an intrinsic property of the group. This is only interesting for infinite groups: every finite group is coarsely equivalent to a point (or the trivial group), since one can choose as finite set of generators the entire group.

Formally, for a given choice of generators, one has the [[word metric]] (the natural distance on the Cayley graph), which determines a [[metric space]]. The coarse [[equivalence class]] of this space is an invariant of the group.