Growth of quasi-convex subgroups in groups with a constricting element
Xabier Legaspi
Consejo Superior de Investigaciones Científicas, Madrid, Spain; Université de Rennes 1, Rennes, France
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Abstract
Given a group acting by isometries on a metric space , we consider a preferred collection of paths of the space , a path system, and study the spectrum of relative exponential growth rates and quotient exponential growth rates of the infinite index subgroups of that are quasi-convex with respect to this path system. If contains a constricting element with respect to the same path system, we are able to determine when the growth rates of the first kind are strictly smaller than the growth rate of , and when the growth rates of the second kind coincide with the growth rate of . Examples of applications include relatively hyperbolic groups, groups, and hierarchically hyperbolic groups containing a Morse element.
Cite this article
Xabier Legaspi, Growth of quasi-convex subgroups in groups with a constricting element. Groups Geom. Dyn. (2024), published online first
DOI 10.4171/GGD/788