I'm looking at a problem in my textbook and it says:

Let $ψ : G_1 → G_2$ be a surjective group homomorphism. Let $H_1$ be a normal subgroup of $G_1$ and suppose that $ψ(H_1) = H_2$. Prove or disprove that $G_1/H_1$ is isomorphic $G_2/H_2$.

So far, I know that since $H_1$ is normal in $G_1$, $H_2$ is also normal in $G_2$. I'm unsure how to proceed from here though, can someone give me a hint?


Question: Should we allow or avoid non-standard pronouns?
Answer: Sure, let them. Who cares about "zis"?  If someone is fond of their own pet thing, let them do it.  They'll have confused people make edits all the time and they'll roll them back and there's no need to have more scuffling than that over it.  I've seen it with "colour vs color" edits, and that's such a waste of time. If someone rejects BC/AD/BCE/CE dates and only puts in years from whatever other frame of reference - fine, let them.

What will happen is that if people insist on making question in their own pet mindframe, few people will answer their question.  As long as people are asking questions they want to know the answer to, this will be self correcting - if you use a language or date system or whatever that people don't understand, you won't get answers. If they are not asking questions they want to know the answer to, crush them, because that's not what we need here.