Permanence properties of the second nilpotent product of groups (Q2295726)

The following results are given. 1) Amenability, the Haagerup property, the Kazhdan property (T) and exactness are preserved under taking second nilpotent product of groups. 2) For two countable groups \(H\) and \(G\) with the Haagerup property, the restricted second nilpotent wreath product \(Hwr_2G\) has also this property. 3) For two countable groups \(A\) and \(G\), if \(A\) is abelian then \(Awr_2G\) is unitarizable if and only if \(G\) is amenable.