Burnside Groups and Related Topics

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IVANOV, 98-01500 The proposer will work on further development and applications of a geometric machinery of graded diagrams which was recently created to solve the famous Burnside problem on periodic groups for all sufficiently large exponents and has already been successfully applied to prove Gromov's conjecture on periodic quotients of hyperbolic groups of bounded exponent. In particular, the proposer will carry out this machinery to free products of groups, investigate finitely presented groups given by periodic relations and subgroups of free Burnside groups of large even exponent, and apply this machinery to nonhyperbolic groups with classical small cancellation conditions. The field of group theory is the mathematical theory of symmetry and interacts with many other disciplines, for example physics and chemistry outside of mathematics, coding theory, number theory and geometry inside mathematics. This research is in combinatorial group theory which studies groups defined by means of generators and defining relations and is the intersection of group theory, low dimensional topology, geometry, and the theory of computability.