# Thread: Another integers mod 4 question

1. ## Another integers mod 4 question

Use the first isomorphism theorem to show the following:

Z/(4Z) is isomorphic to Z4.

There are other ones to solve I'm just using this as an example so I can figure out the thinking behind it. I can prove it with multiplication tables, but in reference to the F.I.T. I'm not sure how to start.

2. Originally Posted by DanielThrice
Use the first isomorphism theorem to show the following:

Z/(4Z) is isomorphic to Z4.

There are other ones to solve I'm just using this as an example so I can figure out the thinking behind it. I can prove it with multiplication tables, but in reference to the F.I.T. I'm not sure how to start.
Possibly because $\theta:\mathbb{Z}\to\mathbb{Z}_4:x\mapsto \left(x\text{ mod }4\right)$ a surjective homomorphism. What's $\ker\theta$?