  In this paper, we obtain analogues of Jorgensen's inequality for
non-elementary groups of isometries of quaternionic hyperbolic $n$-space
generated by two elements, one of which is loxodromic. Our result gives some
improvement over earlier results of Kim [10] and Markham [15]}. These results
also apply to complex hyperbolic space and give improvements on results of
Jiang, Kamiya and Parker [7]
  As applications, we use the quaternionic version of J{\o}rgensen's
inequalities to construct embedded collars about short, simple, closed
geodesics in quaternionic hyperbolic manifolds. We show that these canonical
collars are disjoint from each other. Our results give some improvement over
earlier results of Markham and Parker and answer an open question posed in
[16].
