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.
Please help... No idea how to do this...
Thanks in advance for any help
$\displaystyle a\in\mathbb{Z}/20\mathbb{Z} $ is a unit $\displaystyle \iff (a,20)=1 $.
Therefore the group of units of $\displaystyle \mathbb{Z}/20\mathbb{Z} $ is $\displaystyle \left(\mathbb{Z}/20\mathbb{Z}\right)^\times = \{1,3,7,9,11,13,17,19\} $.
$\displaystyle \left(\mathbb{Z}/4\mathbb{Z}\right)^\times = \{1,3\} $.
Now what kind of map are we talking about here? An isomorphism?