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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Free subgroups of quaternion algebras


Author: Roger C. Alperin
Journal: Proc. Amer. Math. Soc. 118 (1993), 15-17
MSC: Primary 20E08; Secondary 57M07
MathSciNet review: 1123646
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1123646-0
PII: S 0002-9939(1993)1123646-0
Keywords: Free group, Bruhat-Tits tree, quaternion algebra
Article copyright: © Copyright 1993 American Mathematical Society