2-Generator arithmetic Kleinian groups III

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


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.
How to Cite
Conder, M. D. E., Maclachlan, C., Martin, G. J., & O’Brien, E. A. (2002). 2-Generator arithmetic Kleinian groups III. MATHEMATICA SCANDINAVICA, 90(2), 161-179. https://doi.org/10.7146/math.scand.a-14368