I am interested if there is an example of an infinite finitely generated non-amenable group that is residually finite but does not contain non-abelian free subgroups.


What examples of infinite finitely gnerated perfect (non-simple) gropus are non-amenable but do not contain free subgroups?


Many thanks,
Elisabeth



Infinite finitely generated non-amenable groups
Osin and Luck give examples of infinite finitely generated residually finite torsion groups with positive first $\ell^2$-Betti number (and hence non-amenable) in the paper "Approximating the first L2-Betti number of residually finite groups", J. Topol. Anal. 3 (2011), no. 2, 153–160.


<http://www.worldscientific.com/doi/abs/10.1142/S1793525311000532>


