Combinatorial approach for Burnside groups of relatively small odd exponents

We consider a finitely generated group of a given exponent $n$. The bounded Burnside problem, which was stated in 1902, asks whether there exists an infinite such group. The first solution of this problem was given by P. Novikov and S. Adian in their famous work in 1968. They proved that there exists such group for odd exponents $n \geqslant 4381$. After that there was a series of works that decreases a lower bound of the exponent (including works of S. Adian), and a series of works that gives a solution for even $n$ (S. Ivanov, I. Lysenok). Following the spirit of the proof of P. Novikov and S. Adian, in our work we develop a new combinatorial approach for the bounded Burnside problem, which is based on the Rips's idea of the canonical form. We prove that there exist infinite finitely generated groups of odd exponents $n \geqslant 297$.
Joint work with Professor Eliyahu Rips and Professor Katrin Tent.