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In this paper, we study complex hyperbolic triangle groups of type (p₁,p₂,p₃;p₄) with 3≤ p₁≤ p₂≤ p₃≤ p₄≤ ∞. We show that if the element R₁R₂R₃ is elliptic, then the group is either non-discrete or it belongs to a short list of known discrete groups.
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Liao et al. (2026) studied this question.
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