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Abstract reflections and Coxeter groups


Author: David M. Goldschmidt
Journal: Proc. Amer. Math. Soc. 67 (1977), 209-214
MSC: Primary 20H15; Secondary 05C25
DOI: https://doi.org/10.1090/S0002-9939-1977-0463328-2
MathSciNet review: 0463328
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Abstract: A notion of ``abstract reflection'' is introduced and used to characterize the Coxeter groups. Several known results on Coxeter groups are obtained as easy corollaries.


References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Groupes et algèbres de Lie, Chaps. IV, V, VI, Actualités Sci. Indust., No. 1337, Hermann, Paris, 1968. MR 0240238 (39:1590)
  • [2] H. S. M. Coxeter, The complete enumeration of finite groups of the form $ R_i^2 = {({R_i}{R_j})^{{k_{ij}}}} = 1$, J. London Math. Soc. 10 (1935), 21-35.
  • [3] J. Tits, Buildings of spherical type and finite BN pairs, Lecture Notes in Math., vol. 386, Springer-Verlag, New York, 1974. MR 0470099 (57:9866)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0463328-2
Article copyright: © Copyright 1977 American Mathematical Society

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