## If Generators $x, y$ Satisfy the Relation $xy^2=y^3x$, $yx^2=x^3y$, then the Group is Trivial

## Problem 554

Let $x, y$ be generators of a group $G$ with relation

\begin{align*}

xy^2=y^3x,\tag{1}\\

yx^2=x^3y.\tag{2}

\end{align*}

Prove that $G$ is the trivial group.

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