The folner function for Amenable groups Seminar

A group G has a folner sequence if for any n, there exists a sequence V_n of subsets of G, such that the size of the boundary of this set over the size of the set is smaller than 1/n. We can define the folner function f(n) to be the minimum size of a set needed to have |dV_n|/|V_n|<1/n.

A group having a folner function is one of the equivalent definitions of a group being amenable, and in this talk I show that a group having folner function has a finite additive measure. I then calculate the folner growth for products and wreath products of amenable groups, showing these are amenable and how this gives us more information about the group.