I am wondering if anyone could help me with a question I have. The question states: "Describe all homomorphisms from the group $\Bbb Z_4$ to the group $\Bbb Z_8$. "
I'm not sure where to start.
Thanks!
I am wondering if anyone could help me with a question I have. The question states: "Describe all homomorphisms from the group $\Bbb Z_4$ to the group $\Bbb Z_8$. "
I'm not sure where to start.
Thanks!
Hint: Considering $\Bbb Z_4=\{0,1,2,3\}$ with $+$, we'll have that $\phi(1)$, the image of $1$, totally describes all the homomorphism $\phi$. What can $\phi(1)$ be?