Solution
= Solution
{c}
If $G$ is an <abelian group>, its elements commute, so for all $x,y\in G$,
$$
T(xy)=(xy)^3=xyxyxy=x^3y^3=T(x)T(y).
$$
Thus $\boxed{T\text{ is a group homomorphism}}$. Also $T(e)=e^3=e$, as required.
= Solution
{c}
If $G$ is an <abelian group>, its elements commute, so for all $x,y\in G$,
$$
T(xy)=(xy)^3=xyxyxy=x^3y^3=T(x)T(y).
$$
Thus $\boxed{T\text{ is a group homomorphism}}$. Also $T(e)=e^3=e$, as required.