Abstract
It is known that in a word hyperbolic group the stable exponent of every nontorsion element is an integer. We prove that this is also true in finitely generated nilpotent groups. On the other hand, we show that for any rational number ρ≥1 there exists a torsionfree CAT(0) group containing an element whose stable exponent is equal to ρ.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bridson, M. R. and Haefliger, A.: Metric Spaces of Non-positive Curvature, Grundlehren Math. Wiss. 319, Springer-Verlag, Berlin, 1999.
Coornaert, M.:A note on stable exponents, Comm. Algebra 28(11) (2000), 5317–5328.
Gromov, M.:Hyperbolic groups, In: Essays in Group Theory, Math. Sci. Res. Inst. Publ. 8, Springer, New York, 1987, pp. 75–263.
Macdonald, I. D.: The Theory of Groups, Clarendon Press, Oxford, 1968.
Magnus, W., Karrass, A. and Solitar, D.: Combinatorial Group Theory, 2nd edn, Dover Publications, New York, 1976.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Coornaert, M. Stable Exponents in Discrete Groups. Geometriae Dedicata 95, 59–64 (2002). https://doi.org/10.1023/A:1021227311187
Issue Date:
DOI: https://doi.org/10.1023/A:1021227311187