Recurrent points and discrete points for elementary amenable groups

Mostafa Nassar

doi:10.1155/s0161171292000954

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.

Highlights

Let G be a discrete group, M(G) the Banach space of all bounded real valued functions on G with the supremum norm, and M(G)* the conjugate Banach space onM(G)
A group G is called left amenable if there exists a mean on M(G) which is left invariant [4]
If G is an infinite group in EG, G contains an infinite abelian subgroup

Summary

Introduction

Let G be a discrete group, M(G) the Banach space of all bounded real valued functions on G with the supremum norm, and M(G)* the conjugate Banach space onM(G). Let WRG fig- SDG, the set of all weak recurrent points of/G. If G is an infinite group in EG, G contains an infinite abelian subgroup. 2. R0 SETS AND RECURRENT POINTS: c , we will show that .4a Ra and Ra- Ka ://= for any infinite elementary amenable group G. . c PROPOSITION 2.1: If an amenable group G contains an R0-set, Aa Ra and Rc" Ka 7 we.

Results

Conclusion