In my study of group homomorphism I find a question like this.
Let $Q\colon \mathbb Z\to S_8$ be group homomorphism such that $Q(1)=(1,4,2,6)(2,5,7)$. Then find $\ker(Q)$ and $Q(21)$.
In my mind I know that $\ker(Q)$ are those elements of $\mathbb Z$ which map to the identity of $S_8$ .How I can work with this concept to get those elements? Much more difficult I get is to find $Q(21)$.Thank again