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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Free subgroups of quaternion algebras
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by Roger C. Alperin
Proc. Amer. Math. Soc. 118 (1993), 15-17
DOI: https://doi.org/10.1090/S0002-9939-1993-1123646-0

Abstract:

Using the theory of group actions on trees, we shall prove that if a quaternion algebra over Laurant polynomials is not split then a certain congruence subgroup of the group of norm one elements is a free group. This generalizes and gives an easy, conceptually simpler proof than that given by Pollen for the field of real numbers.
References
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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 118 (1993), 15-17
  • MSC: Primary 20E08; Secondary 57M07
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1123646-0
  • MathSciNet review: 1123646