October 5, 2023. A. S. Atkarskaya (The Hebrew University of Jerusalem, Einstein Institute of Mathematics). The Burnside problem: history and new results.

In 1902 W. Burnside asked whether a finitely generated group such that its every element has a finite order is finite. A more restricted question also makes sense: if a finitely generated group with identity xⁿ = 1 is finite. For big enough n (odd n ≥ 557 and even n ≥ 8000) the answer is negative, for n = 2, 3, 4, 6 the answer is positive, for the remaining exponents the answer is unknown. This problem has a direct connection with hyperbolic groups and negative curvature. I will speak about the latest results, explain the methods, and tell where else one can apply these methods.

List of talks at previous sessions of the seminar.