Coxeter Groups and the Bruhat Order

Abstract

In an introductory course on abstract algebra, one will learn about algebraic structures that are seen in many areas of mathematics. In particular, the study of groups include finitely generated groups, the dihedral group, and the symmetric group. This paper will introduce a class of groups called Coxeter groups, which are created by generators and relations. We first present the specific relations of Coxeter groups through matrices and diagrams.