Bijectivity is a great property, which allows to identify (up to isomorphisms!) the given groups. Moreover, a bijective homomorphism of groups $\varphi$ has inverse $\varphi^ {-1}$ which is …

Another way to think about it is that a homomorphism is a map that commutes with multiplication, addition, scaling - or whatever operations characterize your algebraic object. This is actually …

I think that they are similar (or same), but I am not sure. Can anyone explain the difference between isomorphism and homeomorphism?

Aug 16, 2012 · I am still not getting how graph isomorphism and homomorphism differ. Can anyone show me two graphs that are homomorphic, but not isomorphic? Also, Wikipedia says …

Isn't that (your last sentence) what I'm trying to ask? I think I see how to go from a normal subgroup to finding its related homomorphism once I identify its range/image group etc. I'm …

"How are homomorphic images and homomorphisms different?" For starters a homomorphism is a function, while homomorphic image a subset. Have you looked at definitions? What exactly …

Apr 22, 2020 · Finally, in case the solution to the actual problem wasn't clear yet, the strategy you are using should be the right one. The single generator of the pre-image of the ideal will map …

Mar 23, 2017 · Is the homomorphic image of an ideal an ideal? Ask Question Asked 8 years, 8 months ago Modified 3 years, 2 months ago

Oct 30, 2018 · The definition is, it's the image of the field under a homomorphism. So: do you know what field means? do you know what image means? do you know what homomorphism …

Sep 22, 2016 · Prove that the order of homomorphic image divides the order of the group without using First Isomorphism Theorem. Ask Question Asked 9 years, 2 months ago Modified 1 …