Mathematical Sciences: Automorphism Groups of Highly Homogeneous Partially Ordered Sets

本课题研究的是高度齐次的偏序集的自同构群。主要的研究者将集中于几乎所有子群的自由性和高传递性，自由积和合并表示为高传递子群，以及极大子群。他们还将探索实线的自同构群。群是定义了乘法的代数对象。在数学、物理和化学的许多领域中，群体都是自然存在的。每个有限群都可以嵌入到一组排列中。这个项目与无限置换群有关。它涉及群论、逻辑学和组合学。这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.