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.
Coxeter groups. Dominance order. Outer automorphism groups.
AMS Subject Classification (1991)
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