A quantitative Neumann Lemma for finitely generated groups
Résumé
We study the coset covering function $C(r)$ of an infinite, finitely generated group: the number of cosets of infinite index subgroups needed to cover the ball of radius r. We show that $C(r)$ is of order at least $\sqrt{r}$ for all groups. Moreover, we show that $C(r)$ is linear for a class of amenable groups including virtually nilpotent and polycyclic groups, and that it is exponential for property (T) groups.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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