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.
