(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that if [tex]\theta[/tex] is a homomorphism from G onto H, and N [tex]\triangleleft[/tex] G, then [tex]\theta[/tex](N) [tex]\triangleleft[/tex] H.

2. Relevant equations

3. The attempt at a solution

I think I have a good idea of what is going on, but I'm struggling to tie it all together.

It's given that N [tex]\triangleleft[/tex] G so I know that gng[tex]^{-1}[/tex] [tex]\in[/tex] N for all n[tex]\in[/tex]N and all g[tex]\in[/tex]G. I also know that N is a subgroup of G.

I know that [tex]\theta[/tex](G), the image of [tex]\theta[/tex], is a subgroup of H. Because of this, I would also think that [tex]\theta[/tex](N) is also a subgroup of H because of the homomorphism.

From here I need someone to lead me in the right direction. I've been trying to solve this problem for four days so any help is greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof Involving Homomorphism and Normality

**Physics Forums | Science Articles, Homework Help, Discussion**