Følner Sequences in Polycyclic Groups

Abstract

The isoperimetric inequality

\frac{|\partial \Omega|}{|\Omega|} ≥ \frac{\rm constant}{\rm log|\Omega|}

for finite subsets $\Omega$ in a finitely generated group $\Gamma$ with exponential growth is optimal if $\Gamma$ is polycyclic.

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