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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Abstract reflections and Coxeter groups
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by David M. Goldschmidt PDF
Proc. Amer. Math. Soc. 67 (1977), 209-214 Request permission

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
  • 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 [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
  • 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.
  • 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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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