Abstract.
We show that every two-generated torsion-free one-ended word-hyperbolic group has virtually cyclic outer automorphism group. This is done by computing the JSJ-decomposition for two-generator hyperbolic groups. We further prove that two-generated torsion-free word-hyperbolic groups are strongly accessible. This means that they can be constructed from groups with no nontrivial cyclic splittings by applying finitely many free products with amalgamation and HNN-extensions over cyclic subgroups.
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Received June 25, 1998
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Kapovich, I., Weidmann, R. On the structure of two-generated hyperbolic groups. Math Z 231, 783–801 (1999). https://doi.org/10.1007/PL00004753
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DOI: https://doi.org/10.1007/PL00004753