Abstract
We prove the following alternative: either there exists a finitely generated group with exponential growth whose entropy is zero, or there exists a universal constant M>0 such that the entropy of all non-elementary hyperbolic groups with cyclic centralizers and their non-elementary subgroups is at least M. To cite this article: V. Guirardel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 743–746.
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