Geodesic
Comments On a Discreteness Condition for Subgroups of SL(2, C)
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 87-92

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SL(2,C) is the group of all complex unimodular 2 × 2 matrices. A subgroup of SL(2, C) is said to be discrete if it does not contain any convergent sequence of distinct elements. A subgroup is said to be elementary if the commutator of any two elements of infinite order has trace 2. The discreteness condition which this note relates to is the following:PROPOSITION 1. If two complex, unimodular 2 × 2 matrices X and Y generatea non-elementary, discrete group, then 
Jørgensen, Troels. Comments On a Discreteness Condition for Subgroups of SL(2, C). Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 87-92. doi: 10.4153/CJM-1979-010-5
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[1] 1. Jorgensen, T., On discrete groups of Môbius transformations, Amer. J. Math. 98 (1976), 739–749. Google Scholar

[2] 2. Jorgensen, T. and Kiikka, M., Some extreme discrete groups, Ann. Acad. Sci. Fenn., Ser. A. I. Math. 1 (1975), 245–248. Google Scholar

[3] 3. Jorgensen, T., Compact 3-manifolds of constant negative curvature fibering over the circle, Ann. of Math.. 106 (1977), 61–72. Google Scholar

[4] 4. Jorgensen, T., A note on subgroups of SL (2, C), Quart. J. Math. Oxford, (2), 28 (1977), 209–212. Google Scholar

[5] 5. Wielenberg, N., On the fundamental polyhedra of discrete Môbius groups, Amer. J. Math.. 99 (1977), 861–877. Google Scholar

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