Mathematical Sciences: Automorphism Groups of Highly Homogeneous Partially Ordered Sets

研究高度齐次的部分有序集合的自同构群。主要研究了几乎所有子群的自由度和高传递性，合并自由积作为高传递子群的表示，以及极大子群。他们还将探索实线的自同构群。群是在其上定义了乘法的代数对象。在数学、物理和化学的许多领域，群体都是自然存在的。每一个有限群都可以嵌入到一组排列中。本课题涉及无穷置换群。它涉及到群论、逻辑学和组合学。也可能与计算机科学有关。

This project is concerned with the automorphism groups of partially ordered sets which are highly homogeneous. The principal investigators will focus on freeness and high transitivity of almost all subgroups, the representation of free products with amalgamation as highly transitive subgroups, and maximal subgroups. They will also explore the automorphism group of the real line. A group is an algebraic object having a multiplication defined on it. Groups occur naturally in many areas of mathematics, physics and chemistry. Every finite group can be embedded in a group of permutations. This project is concerned with infinite permutation groups. It involves group theory, logic and combinatorics. There are also possible connections with computer science.