Burnside Groups and Related Topics

IVANOV，98-01500 提议者将致力于进一步的发展和应用的几何机械的分级图，最近创建的解决著名的伯恩赛德问题的周期群的所有足够大的指数，并已成功地应用于证明格罗莫夫猜想的周期性双曲群的有界指数。特别地，提出者将执行这一机器的自由产品的群体，调查的周期关系和子群的自由伯恩赛德群的大偶数指数的双曲表示的群体，并应用这一机器的非双曲群与经典的小取消条件。 群论领域是对称性的数学理论，并与许多其他学科相互作用，例如数学之外的物理和化学，编码理论，数论和数学内部的几何。这项研究是在组合群论研究群体定义的发电机和定义关系的手段，是交叉群论，低维拓扑，几何，和理论的可计算性。

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.