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REGULARITY OF QUASIGEODESICS IN A HYPERBOLIC GROUP

    https://doi.org/10.1142/S0218196703001560Cited by:6 (Source: Crossref)

    We prove that for λ≥1 and all sufficiently large ∊, the set of (λ,∊)-quasigeodesics in an infinite word-hyperbolic group G is regular if and only if λ is rational. In fact, this set of quasigeodesics defines an asynchronous automatic structure for G. We also introduce the idea of an exact (λ,∊)-quasigeodesic and show that for rational λ and appropriate ∊ the sets of exact (λ,∊)-quasigeodesics define synchronous automatic structures.

    AMSC: 20F67, 20F10

    References

    • J.   Alonso et al. , Notes on word-hyperbolic groups , Proceedings of the Conference Group Theory from a Geometrical Viewpoint , eds. E.   Ghys , A.   Haefliger and A.   Verjovsky ( World Scientific , Singapore , 1991 ) . Google Scholar
    • D. B. A.   Epstein et al. , Word Processing in Groups ( Jones and Bartlett , Boston , 1992 ) . CrossrefGoogle Scholar
    • W. D. Neumann and M. Shapiro, Int. J. Algebra Comput. 2, 443 (1992). LinkGoogle Scholar
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