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. …

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 …

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

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 …

A homomorphism is a special kind of map between two groups because homomorphism respect the group operation. An isomorphism is a bijective map which maintain the equivalence of the …

May 4, 2019 · To be more precise, there is a one-to-one correspondence between isomorphism types of homomorphic images of G G and normal subgroups of G G.

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 …

Sep 22, 2016 · Prove that the order of homomorphic image divides the order of the group without using First Isomorphism Theorem. Ask Question Asked 8 years, 9 months ago Modified 1 …

Let m m and n n be two given positive integers such that m <n m <n. Then what are the necessary and sufficient conditions for the groups (Zm,+m) (Z m, + m) and (Zn,+n) (Z n, + n) to …