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We study the discreteness for non-elementary subgroup G in PU(1, n;C), underthe assumption that G satisfies Condition A. Mainly, we present that one canuse a test map, which need not to be in G, to examine the discreteness of G,and also show that G is discrete, if every two-loxodromic-generator subgroup ofG is discrete.

Test Map and Discreteness Criteria for Subgroups in PU(1,n;C)