The *Burnside problem* asks whether it is possible for a finitely generated group to be infinite if all its elements have finite order. This version is usually called the *General Burnside problem* and an example of such a group was found in 1964.

The *Burnside group* *B*(*d*, *n*) is the largest *d* generator group in which every element satisfies *x*^{n} = 1.

The *Restricted Burnside problem* asks whether, for fixed *d* and *n*, there is a largest **finite** *d* generator group in which every element satisfies *x*^{n} = 1. A positive solution to the Restricted Burnside problem would show that there are only finitely many finite factor groups of *B*(*d*, *n*).