Solution
= Solution
Substitution sends the defining relation to
$$
t(a^2)^2t^{-1}=ta^4t^{-1}=(ta^2t^{-1})^2=a^6=(a^2)^3.
$$
Thus the assignment respects the relator and extends to a <group homomorphism> $\boxed{\theta:S\to S}$.
= Solution
Substitution sends the defining relation to
$$
t(a^2)^2t^{-1}=ta^4t^{-1}=(ta^2t^{-1})^2=a^6=(a^2)^3.
$$
Thus the assignment respects the relator and extends to a <group homomorphism> $\boxed{\theta:S\to S}$.