We show that for arbitrary fixed conjugacy classes C1, ..., Cl, l ≥ 3, of loxodromic isometries of the two-dimensional complex or quaternionic hyperbolic space there exist isometries g1, ..., gl, where each gi∈ Ci, and whose product is the identity. The result follows from the properness, up to conjugation, of the multiplication map on a pair of conjugacy classes in rank 1 groups. © 2009 Elsevier B.V.
Falbel, E., & Wentworth, R. A. (2009). On products of isometries of hyperbolic space. Topology and Its Applications, 156(13), 2257–2263. https://doi.org/10.1016/j.topol.2009.05.013