A hyperbolic-by-hyperbolic hyperbolic group

Mosher, Lee

doi:10.1090/S0002-9939-97-04249-4

A hyperbolic-by-hyperbolic hyperbolic group
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Proc. Amer. Math. Soc. 125 (1997), 3447-3455 Request permission

Abstract:

Given a short exact sequence of finitely generated groups \[ 1 \to K \to G \to H \to 1 \] 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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