2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66385In this paper we give necessary and sufficient conditions for discreteness of a group generated by a hyperbolic element and an elliptic one of odd order. This completes the classification of discrete groups with non-$π$-loxodromic generators in the class of two-generator groups with real parameters. The criterion is given also as a list of all parameters that correspond to discrete groups. An interesting corollary of the result is that the group of the minimal known volume hyperbolic orbifold has real parameters.43 pages, 26 figures; minor changes; Table 2 is correctedGroup Theory30F40; 57S30; 20H10text