Showing non-amenability of a (non-abelian) free group is somewhat easy and one can do this immediately after the definition of amenability. Is there an easy proof of the fact that free groups do not ...
Is Kazhdan's property (T) stable under extensions? i.e. if $G$ is an extension of a group with property (T) by a group with property (T), does it follow that $G$ has property (T)?