I'm reading a paper and I'm uncertain about one of its claims. I was wondering if someone could clarify. Namely, it states that for a discrete subgroup of $\text{Isom } H^n$, the finite order elements are the elliptic isometries. My question is why can we not have any finite order loxodromic or parabolic isometries also be elements in this subgroup?
EDIT: For reference I am reading "Geometrical Finiteness for Hyperbolic Groups"