2-Generator arithmetic Kleinian groups III

Authors

  • M. D. E. Conder
  • C. Maclachlan
  • G. J. Martin
  • E. A. O'Brien

DOI:

https://doi.org/10.7146/math.scand.a-14368

Abstract

This paper forms part of the program to identify all the 2-generator arithmetic Kleinian groups. Here we identify all conjugacy classes of such groups with one generator parabolic and the other generator elliptic. There are exactly $14$ of these and exactly $5$ Bianchi groups in their commensurability class, namely $\mathrm{PSL}(2,{\mathcal O}_d)$ for $d=1,2,3,7$ and $15$. This complements our earlier identification of the $4$ arithmetic Kleinian groups generated by two parabolic elements.

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Published

2002-06-01

Issue

Vol. 90 No. 2 (2002)

Section

Articles

How to Cite

[1]
M. D. E. Conder, C. Maclachlan, G. J. Martin, and E. A. O'Brien, “2-Generator arithmetic Kleinian groups III”, Math. Scand., vol. 90, no. 2, pp. 161–179, Jun. 2002, doi: 10.7146/math.scand.a-14368.