In our most recent meeting, we discussed a pretty hefty chapter that covers homomorphisms and the first isomorphism theorem (along with some other results), which is one of the more important theorems from group theory. Then we worked on two exercises from the chapter that asked us to use the first isomorphism theorem to prove the second and third isomorphism theorems.

To begin, I’ll just include a statement of the first isomorphism theorem:

Now, we were tasked with the following two exercises:

Our line of reasoning for the second isomorphism theorem was as follows:

And for the third: