Genre
Journal ArticleDate
2015-01-01Author
Chinburg, TFriedlander, H
Howe, S
Kosters, M
Singh, B
Stover, M
Zhang, Y
Ziegler, P
Subject
S-unit groupsS-arithmetic lattices
presentations for S-arithmetic lattices
Hurwitz order
congruence subgroup problem
Permanent link to this record
http://hdl.handle.net/20.500.12613/5833
Metadata
Show full item recordDOI
10.1080/10586458.2014.968269Abstract
© 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.Citation to related work
Informa UK LimitedHas part
Experimental MathematicsADA compliance
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http://dx.doi.org/10.34944/dspace/5815