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Presentations for quaternionic S-unit groups
Chinburg, T Friedlander, H Howe, S Kosters, M Singh, B Stover, M Zhang, Y Ziegler, P
Chinburg, T
Friedlander, H
Howe, S
Kosters, M
Singh, B
Stover, M
Zhang, Y
Ziegler, P
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Journal Article
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2015-01-01
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10.1080/10586458.2014.968269
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© 2015 Taylor and Francis Group, LLC. We give an algorithm for presenting S-unit groups of an order in a definite rational quaternion algebra B such that for every p S at which B splits, the localization of at p is maximal, and all left ideals of of norm p are principal. We then apply this to give presentations for projective S-unit groups of the Hurwitz order in Hamiltons quaternions over the rational field. To our knowledge, this provides the first explicit presentations of an S-arithmetic lattice in a semisimple Lie group with S large. We also include some discussion and experimentation related to the congruence subgroup problem, which is open for S-units of the Hurwitz order when S contains at least two odd primes.
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Informa UK Limited
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Experimental Mathematics
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