Proc. Japan Acad. Ser. A Math. Sci. 93 (7), 67-71, (July 2017) DOI: 10.3792/pjaa.93.67
KEYWORDS: Complex hyperbolic triangle group, complex involution, 22E40, 32Q45, 51M10
A complex hyperbolic triangle group is a group generated by three complex involutions fixing complex lines in complex hyperbolic space. In our previous papers~[4,5,6,7,8] we discussed complex hyperbolic triangle groups. In particular, in~[5,8] we considered complex hyperbolic triangle groups of type $(n,n,\infty;k)$ and proved that for $n \geq 22$ these groups are not discrete. In this paper we show that if $n \geq 14$, then complex hyperbolic triangle groups of type $(n,n,\infty;k)$ are not discrete and give a new list of non-discrete groups of type $(n,n,\infty;k)$.