A hyperbolic-by-hyperbolic hyperbolic group

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Given a short exact sequence of finitely generated groups 1 → K → G →H → 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.

Original languageEnglish (US)
Pages (from-to)3447-3455
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number12
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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