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Higher torsion in the abelianization of the full bianchi groups

Rahm, Alexander D.
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Publication Date
2013-01-01
Keywords
imaginary quadratic integers, elliptic-curves, homology, psl2, cohomology, reduction
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Article
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Citation
Rahm, Alexander D. (2013). Higher torsion in the abelianization of the full bianchi groups. LMS Journal of Computation and Mathematics 16 , 344-365
Abstract
Denote by Q(root-m), with m a square-free positive integer, an imaginary quadratic number field, and by O-m its ring of integers. The Bianchi groups are the groups SL2(O-m). In the literature, so far there have been no examples of p-torsion in the integral homology of the full Bianchi groups, for p a prime greater than the order of elements of finite order in the Bianchi group, which is at most 6. However, extending the scope of the computations, we can observe examples of torsion in the integral homology of the quotient space, at prime numbers as high as for instance p = 80 737 at the discriminant -1747.
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Publisher
Oxford University Press (OUP)
Publisher DOI
10.1112/s1461157013000168
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)