Burnside Groups and Related Topics

伯恩赛德团体及相关主题

• 批准号: 9801500
• 负责人: Sergei Ivanov
• 金额: $ 11.25万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-05-15 至 2001-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801500&HistoricalAwards=false
• 关键词: Burnside; Groups; Related; Topics

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.

Ivanov，98-01500作者将致力于分次图几何机制的进一步发展和应用，它是最近创建的，用来解决所有足够大的指数的周期群上著名的Burnside问题，并已成功地应用于证明Gromov关于有界指数双曲群的周期商的猜想。特别地，作者将对群的自由积执行这一机制，研究由周期关系给出的有限呈现群和大偶数指数自由Burnside群的子群，并将这一机制应用于具有经典小消去条件的非双曲群。群论领域是对称的数学理论，并与许多其他学科相互作用，例如数学之外的物理和化学，数学中的编码论、数论和几何。这项研究是组合群论，它研究用生成元和定义关系定义的群，是群论、低维拓扑、几何和可计算性理论的交集。