The two generator restricted Burnside group of exponent five

In 1902 Burnside [4] wrote "A still undecided point in the theory of discontinuous groups is whether the order of a group may be not finite while the order of every operation it contains is finite". This leads to the following problem, now called the Burnside problem: "If a group is finitely generated and of finite exponent, is it finite?" This is a very difficult question so a weaker form known as the restricted Burnside problem has also been investigated. The restricted Burnside problem is "Given integers n and r is there a largest finite group B(n, r) with v generators and exponent n ?" Of course an affirmative answer to the Burnside problem is automatically an affirmative answer to the restricted Burnside problem.