A quantitative Neumann Lemma for finitely generated groups - Archive ouverte HAL
Article Dans Une Revue Israel Journal of Mathematics Année : 2023

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.
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Dates et versions

hal-03886679 , version 1 (06-12-2022)
hal-03886679 , version 2 (05-07-2023)

Identifiants

Citer

Elia Gorokhovsky, Nicolás Matte Bon, Omer Tamuz. A quantitative Neumann Lemma for finitely generated groups. Israel Journal of Mathematics, In press, ⟨10.1007/s11856-024-2617-x⟩. ⟨hal-03886679v2⟩
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