Back Théorie combinatoire des groupes French Teoria combinatória de grupos Portuguese Комбинаторная теория групп Russian Комбінаторна теорія груп Ukrainian Lý thuyết nhóm tổ hợp Vietnamese
In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and 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.