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A hyperbolic-by-hyperbolic hyperbolic group


Author: Lee Mosher
Journal: Proc. Amer. Math. Soc. 125 (1997), 3447-3455
MSC (1991): Primary 20F32; Secondary 57M07, 20F28
DOI: https://doi.org/10.1090/S0002-9939-97-04249-4
MathSciNet review: 1443845
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Abstract: Given a short exact sequence of finitely generated groups

\begin{displaymath}1 \to K \to G \to H \to 1 \end{displaymath}

it is known that if $K$ and $G$ are word hyperbolic, and if $K$ is nonelementary, then $H$ is word hyperbolic. In the original examples due to Thurston, as well as later examples due to Bestvina and Feighn, the group $H$ is elementary. We give a method for constructing examples where all three groups are nonelementary.


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Additional Information

Lee Mosher
Affiliation: Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102
Email: mosher@andromeda.rutgers.edu

DOI: https://doi.org/10.1090/S0002-9939-97-04249-4
Received by editor(s): May 4, 1996
Additional Notes: Partially supported by NSF grant # DMS-9204331
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

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