Weakly recurrent and almost periodic points in βG

Abstract

Let G be a group. We will study the relationship between AG and WRG. In Nassar [1] it has been shown that if G is a nontorsion group, then AG⫋RG. In this paper we will show that if G contains a subset A such that K.A is not left thick for each finite set K and A is not a finite union of thin sets, then AG⫋WRG.