6 Chordal Coxeter Groups

Complete Growth Series of Coxeter Groups with more than Three Generators

On the Isomorphism Problem for Finitely Generated Coxeter Groups. I Basic Matching

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper, we determine some stro...

Quotient Isomorphism Invariants of a Finitely Generated Coxeter Group

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [4] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper we describe a family of...

Matching Theorems for Systems of a Finitely Generated Coxeter Group

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. For a recent survey, see Mühlherr [10...

The Even Isomorphism Theorem for Coxeter Groups

Coxeter groups have presentations 〈S : (st)st∀s, t ∈ S〉 where for all s, t ∈ S, mst ∈ {1, 2, . . . ,∞}, mst = mts and mst = 1 if and only if s = t. A fundamental question in the theory of Coxeter groups is: Given two such “Coxeter” presentations, do they present the same group? There are two known ways to change a Coxeter presentation, generally referred to as twisting and simplex exchange. We ...