Recurrent points and discrete points for elementary amenable groups

Abstract

Let βG be the Stone-Cech compactification of a group G, AG the set of all almost periodic points in βG, KG=cℓ[⋃{suppμφ:φ∈LIM(G)}] and RG the set of all recurrent points in βG. 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≠ϕ.