MathNet 2016-part-03 — 184 problems (EN–VI) Question 166

Let $G$ be a group and $x, y \in G$ with the property that ord $(x)=3$, $y^{4}=e$, $x y=y^{3} x$. Show that if $y \in G \setminus \{e\}$ then ord $(y)=2$ and $x y=y x$.