In many areas, it's more useful to study structure-preserving maps on an object, rather than just the object itself; this can encode additional information about the structure and its restrictions. …

This is much stronger than one group being a homomorphic image of another, because one can lose lots of information about a group in the kernel of a homomorphism (just take π: G → G/N …

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

Nov 2, 2015 · Maybe you also want to mention that the term homomorphic is completely useless as any two groups will be homomorphic.

"Homomorphism" means different things depending on what objects you're thinking about, and one of those things is the same as "linear map." Namely, for a field k k, a k k -linear map …

Oct 30, 2018 · 1 What is Homomorphic image of a field? How to define it? Can anyone please make me understand? I was trying to prove the theorem F F can have only two homomorphic …

"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 …

Dec 5, 2019 · The general strategy for determining all homomorphic images of a group G G is to find all normal subgroups of G G and determine the groups obtained by taking the quotient of …

Jan 4, 2015 · Show that Z9 Z 9 is not the homomorphic image of Z3 × Z3 Z 3 × Z 3. Ask Question Asked 10 years, 5 months ago Modified 1 year, 9 months ago

G/N G / N being the homomorphic image of G/G′ G / G ′ means that there is a surjective homomorphism φ: G/G′ → G/N φ: G / G ′ → G / N. The existence of such homomorphism is an …