The following question is proposed in [4, Question 1.20]: Let $G$ be a compact group, and suppose that $$\mathcal{N}_k(G) = \{(x1,\dots,x_{k+1}) \in G^{k+1} \;\|; [x_1,\dots, x_{k+1}] 1\}$$ has positive Haar measure $G^{k+1}$. Does have an open $k$-step nilpotent subgroup? case $k 1$ already known. We positively answer it for 2$.