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On outer automorphism groups of coxeter groups

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Summary

It is shown that the outer automorphism group of a Coxeter groupW 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 andΠ 1 andΠ 2 any two bases of the root system ofW, thenΠ 2 = ±ωΠ 1 for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, 2006, NSW, Australia

    R. B. Howlett & D. E. Taylor

  2. Department of Mathematics, University of Manchester Institute of Science and Technology, M60 1QD, Manchester, United Kingdom

    P. J. Rowley

Authors
  1. R. B. Howlett
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  2. P. J. Rowley
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  3. D. E. Taylor
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This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.

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Howlett, R.B., Rowley, P.J. & Taylor, D.E. On outer automorphism groups of coxeter groups. Manuscripta Math 93, 499–513 (1997). https://doi.org/10.1007/BF02677488

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  • DOI: https://doi.org/10.1007/BF02677488

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