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In this paper, we obtain analogues of Jørgensen&#39;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 and Markham. These results also apply to complex hyperbolic space and give improvements on results of Jiang, Kamiya and Parker. As applications, we...

JORGENSEN'S INEQUALITY AND COLLARS IN n-DIMENSIONAL QUATERNIONIC HYPERBOLIC SPACE