Automorphisms of Coxeter groups of rank three

Abstract

If W W is an infinite rank 3 3 Coxeter group, whose Coxeter diagram has no infinite bonds, then the automorphism group of W W is generated by the inner automorphisms and any automorphisms induced from automorphisms of the Coxeter diagram. Indeed Aut ⁡ ( W ) \operatorname {Aut}(W) is the semi-direct product of Inn ⁡ ( W ) \operatorname {Inn}(W) and the group of graph automorphisms.