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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Automorphisms of Coxeter groups of rank three


Authors: W. N. Franzsen and R. B. Howlett
Journal: Proc. Amer. Math. Soc. 129 (2001), 2607-2616
MSC (2000): Primary 20F55
Published electronically: February 15, 2001
MathSciNet review: 1838783
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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 $\operatorname{Aut}(W)$is the semi-direct product of $\operatorname{Inn}(W)$ and the group of graph automorphisms.


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Additional Information

W. N. Franzsen
Affiliation: Australian Catholic University, 25A Barker Rd, Strathfield, New South Wales 2135, Australia
Email: b.franzsen@mary.acu.edu.au

R. B. Howlett
Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
Email: R.Howlett@maths.usyd.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05878-6
PII: S 0002-9939(01)05878-6
Received by editor(s): December 1, 1999
Received by editor(s) in revised form: January 31, 2000
Published electronically: February 15, 2001
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society