c©1997 American Mathematical Society

Abstract. If W is an infinite rank 3 Coxeter group, whose Coxeter diagram has no infinite bonds, then the automorphism group of W is generated by the inner automorphisms and any automorphisms induced from automorphisms of the Coxeter diagram. Indeed Aut(W) is the semi-direct product of Inn(W) and the group of graph automorphisms. 1. Preliminaries The main aim of this paper is to prove the following result. Theorem 1. If W is an infinite, rank 3, Coxeter group, whose Coxeter diagram has no infinite bonds, then the automorphism group of W is the semi-direct product of Inn(W) and the group of graph automorphisms. We recall that a Coxeter group is a group with a presentation of the form W = gp 〈 { ra | a ∈ Π} | (rarb)mab = 1 for all a, b ∈ Π 〉 where Π is some indexing set, whose cardinality is called the rank of W, and the parameters mab satisfy the following conditions: mab = mba, each mab lies in the set {m ∈ Z | m ≥ 1} ∪ {∞} and mab = 1 if and only if a = b. In this paper w