Følner Sequences in Polycyclic Groups

Abstract

The isoperimetric inequality

\frac{∣ \partial Ω∣}{∣Ω∣} \geq \frac{constant}{log∣Ω∣}

for finite subsets $Ω$ in a finitely generated group $Γ$ with exponential growth is optimal if $Γ$ is polycyclic.

Christophe Pittet, Følner Sequences in Polycyclic Groups. Rev. Mat. Iberoam. 11 (1995), no. 3, pp. 675–685