On Outer Automorphism Groups of Coxeter Groups


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


Research Report 96-26
Date: 20 June 1996


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


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