Recurrent points and discrete points for elementary amenable groups (Q1205614)

Let \(\beta G\) be the Stone-Čech compactification of a discrete group, \(A^ G\), the set of almost periodic points in \(\beta G\), \(K^ G\) the closure of the union of all supports of left invariant means on \(M(G)\) (bounded functions) considered as measures on \(\beta G\) and \(R^ G\) the set of all recurrent points. Motivated by papers of \textit{C. Chou} [Ill. J. Math. 22, 54-63 (1978; Zbl 0373.28008) (\(G =\mathbb{Z}\)) and ibid. 24, 396- 407 (1980; Zbl 0439.20007)], the author studies relations between these sets and proves for any infinite elementary amenable group that: \(A^ G \subsetneqq R^ G\) and \(R^ G\setminus K^ G \neq \emptyset\).