A non-abelian, non-Sidon, completely bounded $\mathrm{\Lambda }(p)$ set

The purpose of this note is to construct an example of a discrete non-abelian group $G$ and a subset $E$ of $G$, not contained in any abelian subgroup, that is a completely bounded $\mathrm{\Lambda }(p)$ set for all $p<\mathrm{\infty },$ but is neither a Leinert set nor a weak Sidon set.