LMS Journal of Computation and Mathematics

Research Article

Higher torsion in the Abelianization of the full Bianchi groups

Alexander D. Rahm

Department of Mathematics, National University of Ireland at Galway,Ireland email Alexander.Rahm@nuigalway.ie

Abstract

Denote by , with a square-free positive integer, an imaginary quadratic number field, and by its ring of integers. The Bianchi groups are the groups . In the literature, so far there have been no examples of -torsion in the integral homology of the full Bianchi groups, for 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 at the discriminant .

Supplementary materials are available with this article.

(Received January 18 2013)

(Revised May 16 2013)

(Online publication September 2013)

2010 Mathematics Subject Classification

  • 11F75 (primary)

Footnotes

  Funded by the Irish Research Council.