On the structure of two-generated hyperbolic groups |
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| Authors: | Ilya Kapovich Richard Weidmann |
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| Institution: | Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA (e-mail: ilia@math.rutgers.edu), US
Fakult?t für Mathematik, Ruhr-Universit?t Bochum, D-44780 Bochum, Germany (e-mail: Richard.Weidmann@ruhr-uni-bochum.de), DE
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| 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.
Received June 25, 1998 |
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