Abstract
In the paper [12], Yang conjectured that a nonelementary subgroup G of SL(2,C) containing elliptic elements is discrete if for eacch elliptic element g ∈ G the group is discrete, where f ∈ SL(2, C) is a test map being loxodromic or elliptic. By embedding SL(2, C) into U(1, 1;H), we give an affirmative answer to this question. As an application, we show that a nonelementary and nondiscrete subgroup of Isom(H^3) must contain an elliptic element of order at least 3.
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