Complexity amongst the finitely generated subgroups of Thompson's Group

这个项目的目的是探索在广义R中的群（和群的子群）的结构。Thompson群族，在各种复杂性约束下。广义R. Thompson群族代表了一类重要的群，其中这些群的理论通常与数学的各个领域（包括拓扑学、分析、逻辑和动力学）有联系和应用。我们考虑的复杂性约束有各种类型：例如，探索R的初等顺从子群的结构。Thompson群F，研究了在增长条件下的群或子群，计算群元素，考虑了R的那些子群的子群结构。汤普森的群T或V，其中不包含非阿贝尔自由子群，了解交换子宽度在任何R。Thompson群或它们的推广，决定Thurston的分段积分射影群的边界群（R。Thompson的组T）是否是随机生成的，等等。SMSTC课程; ID 5101;学校研讨会

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