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On generalized Jørgensen inequality in \(\operatorname{SL}(2,\mathbb{C})\). (English) Zbl 1421.30057

Summary: H. Wang et al. [Proc. Indian Acad. Sci., Math. Sci. 123, No. 2, 245–251 (2013; Zbl 1280.20055)] have obtained a generalized version of the Jørgensen inequality for two generator subgroups of \(\operatorname{SL}(2,\mathbb{C})\) where one of the generators is loxodromic. We prove that their inequality is strict.

MSC:

30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)

Citations:

Zbl 1280.20055
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References:

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