1. ## Homomorphism

find all homomorphism form Z6 to Z4?

2. Originally Posted by mathemanyak
find all homomorphism form Z6 to Z4?
Hint: Any homomorphism is completely determined on $[1]_6$ because $\left< [1]_6\right> = \mathbb{Z}_6$.

Now there are four possbilites:
$[1]_6\mapsto [0]_4$
$[1]_6\mapsto [1]_4$
$[1]_6\mapsto [2]_4$
$[1]_6\mapsto [3]_4$

Now check which ones are isomorphisms.