Recurrent points and discrete points for elementary amenable groups

Let 2G be the Stone-Cech compactification of a group G, AG the set of all almost periodic points in 2G, KG=c ￠ “[ ￠ {supp : ￠ LIM(G)}] and RG the set of all recurrent points in 2G. In this paper we will study the relationships between KG and RG, and between AG and RG. We will show that for any infinite elementary amenable group G, AG ￠ RG and RG ￠ ’KG ￠ ‰ .