Editing Combinatorial group theory (section)

In [[mathematics]], '''combinatorial group theory''' is the theory of [[free group]]s, and the concept of a [[presentation of a group]] by [[generator (mathematics)|generators]] and [[relation (mathematics)|relations]]. It is much used in [[geometric topology]], the [[fundamental group]] of a [[simplicial complex]] having in a natural and geometric way such a presentation.
A very closely related topic is [[geometric group theory]], which today largely subsumes combinatorial group theory, using techniques from outside combinatorics besides.

It also comprises a number of [[algorithmically insoluble]] problems, most notably the [[word problem for groups]]; and the classical [[Burnside problem]].