# On Outer Automorphism Groups of Coxeter Groups

## Authors

**R. B. Howlett**, **P. J. Rowley** and **D. E. Taylor**

## Status

Research Report 96-26

Date: 20 June 1996

## Abstract

It is shown that the outer automorphism group of a Coxeter group W
of finite rank is finite if the Coxeter graph contains no infinite
bonds. A key step in the proof is to show that if the group is
irreducible and Pi1 and Pi2 any two bases of the root system
of W, then Pi2 = +- w Pi1 for some w in W. The proof of this
latter fact employs some properties of the dominance order on the root
system introduced by Brink and Howlett.

## Key phrases

Coxeter groups. Dominance order. Outer automorphism groups.

## AMS Subject Classification (1991)

Primary: 20F55
Secondary: 20F28

## Content

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