The synchronisation hierarchy of permutation groups

排列群的同步层次

• 批准号: DP200101951
• 负责人: A/Prof John Bamberg
• 金额: $ 28.09万
• 依托单位: The University of Western Australia
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-07-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200101951
• 关键词: synchronisation; hierarchy; permutation; groups

This project aims to make significant advances in understanding finite primitive permutation groups, which are the basic building blocks of the mathematical study of symmetry. A recently-developed perspective, inspired by the notion of a synchronising automaton, has revealed that these groups fall into a natural hierarchy. While the outline of this synchronisation hierarchy is known, many questions remain about exactly which primitive groups lie in which layers. Answering these questions using techniques from group theory, graph theory and finite geometry will substantially deepen our understanding. The benefits of this include new knowledge and enhanced insight into this fundamental class of groups and new tools for their analysis.

这个项目的目的是在理解有限本原置换群方面取得重大进展，这是对称性数学研究的基本组成部分。最近发展的观点，灵感来自同步自动机的概念，揭示了这些群体落入一个自然的层次结构。虽然这个同步层次的轮廓是已知的，但关于哪些原始群位于哪些层中的问题仍然存在。 利用群论、图论和有限几何的技巧来解决这些问题将大大加深我们的理解。这样做的好处包括新的知识和增强对这类基本群体的洞察力以及用于分析它们的新工具。