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This research was done independently by Hoare and Karrass-Solitar and was supported in part by grants from the National Research Council of Canada.
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Hoare, A.H.M., Karrass, A. & Solitar, D. Subgroups of infinite index in Fuchsian groups. Math Z 125, 59–69 (1972). https://doi.org/10.1007/BF01111114
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DOI: https://doi.org/10.1007/BF01111114