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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Abstract reflections and Coxeter groups

Author: David M. Goldschmidt
Journal: Proc. Amer. Math. Soc. 67 (1977), 209-214
MSC: Primary 20H15; Secondary 05C25
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, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968 (French). MR 0240238
  • [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] Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099

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Article copyright: © Copyright 1977 American Mathematical Society