A note on the Følner condition for amenability

Abstract

Let G be a countably generated discrete group. A right-invariant mean μ on G is a bounded linear functional of the space L∞(G) of bounded functions on G having the property:We say that G is amenable if it is equipped with a right-invariant mean. Finite groups, abelian groups, in fact, groups of subexponential growth are amenable. Solvable group are also amenable. Subgroups and quotients of amenable groups are amenable. On the other hand, free groups having two generators and over are non-amenable.