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Free subgroups of $$SL_ 2({\mathbb{C}})$$ with two parabolic generators. (English) Zbl 0639.20025
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 155, 150-155 (Russian) (1986; Zbl 0624.20030).
##### MSC:
 20G20 Linear algebraic groups over the reals, the complexes, the quaternions 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 20E07 Subgroup theorems; subgroup growth 20E05 Free nonabelian groups 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) 22E40 Discrete subgroups of Lie groups
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##### References:
 [1] R. Lyndon and J. Ullman, ?Groups generated by two parabolic linear fractional transformations,? Can. J. Math.,21, No. 6, 1388?1403 (1969). · Zbl 0191.01904 · doi:10.4153/CJM-1969-153-1 [2] D. Sullivan, ?Quasiconformal homeomorphisms and dynamics. II,? Acta Math.,155, No. 3?4, 243?260 (1985). · Zbl 0606.30044 · doi:10.1007/BF02392543 [3] L. R. Ford, Automorphic Functions [Russian translation], Moscow (1936). [4] N. A. Gusevskii and N. S. Zindinova, ?Characterization of extended Schottky groups,? Dokl. Akad. Nauk SSSR,286, No. 5, 1054?1057 (1986). [5] B. Maskit, ?On the classification of Kleinian groups. II,? Acta Math.,138, No. 1?2, 17?42 (1977). · Zbl 0358.30011 · doi:10.1007/BF02392312 [6] D. Sullivan, ?Quasiconformal homeomorphisms and dynamics. III,? Preprint, 1982. [7] V. Chuckrow, ?On Schottky groups with applications to Kleinian groups,? Ann. Math.,88, No. 1, 47?61 (1968). · Zbl 0186.40603 · doi:10.2307/1970555 [8] A. Berdon, Geometry of Discrete Groups [Russian translation], Moscow (1986). [9] P. Blanchard, ?Complex analytic dynamics on the Riemann sphere,? Bull. Am. Math. Soc.,11, No. 1, 85?141 (1984). · Zbl 0558.58017 · doi:10.1090/S0273-0979-1984-15240-6 [10] M. Yu. Lyubich, ?Dynamics of rational transformations: topological picture,? Usp. Mat. Nauk,41, No. 4, 35?95 (1986). [11] R. J. Evans, ?Non-free groups generated by two parabolic matrices,? J. Res. Nat. Bureau of Standards,84, No. 2, 179?180 (1979). · Zbl 0414.20028 · doi:10.6028/jres.084.007
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