Mathematical Sciences: Automorphism Groups of Highly Homogeneous Partially Ordered Sets

这个项目关注的是 高度齐次的偏序集。 的 主要研究人员将专注于自由度和高 几乎所有子群的传递性，自由子群的表示 产品与合并作为高传递子群，和 极大子群 他们还将探索自同构群 真实的线。 群是一个代数对象， 在许多领域， 数学物理和化学。 每个有限群都可以是 嵌入在一组排列中。 这个项目关注的是 无限置换群 它涉及到群论， 逻辑学和组合学 也有可能的联系 计算机科学。

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.