Let $G$ be group and $x\otimes[y,z] =([x,y]\otimes z)^2$, for any $x,y,z\in G$. Then prove $$[x,y]\otimes y=1_{\otimes},$$ for any $x,y\in G$.
This is a part of Corollary 4 in page 82 in the article of P. Moravec, On nonabelian tensor analogues of 2-Engel condition, Glasgow Math. J. 47 (2005) 77-86.
Thank you