2-Generator arithmetic Kleinian groups III

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

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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DOI: http://dx.doi.org/10.7146/math.scand.a-14368

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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