Complexity amongst the finitely generated subgroups of Thompson's Group

汤普森群的有限生成子群之间的复杂性

• 批准号: 2275823
• 金额: --
• 依托单位: University of St Andrews
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2275823
• 关键词: Complexity; amongst; finitely; generated; subgroups

This project is aimed at exploring the structure of groups (and of subgroups of groups) in the generalised R. Thompson family of groups, under various complexity constraints. The generalised R. Thompson family of groups represents an important class of groups, where the theory of these groups often has connections and applications to/in various areas of mathematics including topology, analysis, logic, and dynamics.The complexity constraints we have in mind are of various types: E.g., exploring the structure of the elementary amenable subgroups of R. Thompson group F, exploring groups or subgroups under growth conditions for counting group elements, considering the subgroup structure of those subgroups of R. Thompson's groups T or V which contain no non-abelian free subgroups, understanding commutator width in any of the R. Thompson groups or their generalisations, deciding if the boundary groups for Thurston's Piecewise Integral Projective groups (natural generalisations of R. Thompson's group T) are finitely generated or not, and etc.SMSTC courses; ID5101; school seminars

该项目旨在探索在各种复杂性约束下广义 R. Thompson 群族中群（以及群的子群）的结构。广义 R. Thompson 群族代表了一类重要的群，这些群的理论通常与拓扑、分析、逻辑和动力学等各个数学领域有联系和应用。我们所考虑的复杂性约束有多种类型：例如，探索 R. Thompson 群 F 的基本顺应子群的结构，探索在增长条件下计算群元素的群或子群，考虑到 不包含非交换自由子群的 R. Thompson 群 T 或 V 的子群的子群结构，了解任何 R. Thompson 群中的换向器宽度或其推广，决定 Thurston 分段积分射影群（R. Thompson 群 T 的自然推广）的边界群是否是有限生成的，等等。SMSTC 课程； ID5101；学校研讨会