Let $\mathcal{G}$ be a finite group such that $\left ( \left | \mathcal{G} \right | , 3 \right ) =1$. If for the elements $a, \beta \in \mathcal{G}$ holds that
$$\left ( a \beta \right )^3 = a^3 \beta^3$$
then prove that $\mathcal{G}$ is abelian.
Solution
$$\left ( a \beta \right )^3 = a^3 \beta^3$$
then prove that $\mathcal{G}$ is abelian.
Solution