1. ## Units in Z20

Make a list of units in Z20 and verify that they all map to units in Z4. Show that ther is a non-unit in Z20 that maps to a unit in Z4.

Thanks in advance for any help

2. Originally Posted by jzellt
Make a list of units in Z20 and verify that they all map to units in Z4. Show that ther is a non-unit in Z20 that maps to a unit in Z4.

Thanks in advance for any help
$a\in\mathbb{Z}/20\mathbb{Z}$ is a unit $\iff (a,20)=1$.

Therefore the group of units of $\mathbb{Z}/20\mathbb{Z}$ is $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times = \{1,3,7,9,11,13,17,19\}$.

$\left(\mathbb{Z}/4\mathbb{Z}\right)^\times = \{1,3\}$.

Now what kind of map are we talking about here? An isomorphism?

3. I'm not really sure what is meant by "map" either, but thanks for the reply. This will at least get me started...