Abstract Algebra | The Second Isomorphism Theorem for Groups

We present a proof of the second isomorphism theorem for groups.

[mentormaths]

Sir m from Pakistan and really impressed by your knowledge and teaching method... My all concepts are clear now about isomorphism theorems.. I Salute u I didn't understand before when my teacher taught me who took his doctorate degree from germany

[tomjeong]

the more I learn about abstract algebra, the more I appreciate mathematics.. What a beautiful proof

[ihebbendebba]

i have been sweeping through books and manuals the entire day and you are the only person i found on the internet who explained it thoroughly. thanks for everything.

[cl]

Thank you very much. Unmatched clarity on this difficult topic at least for me

[LwLevel]

Good job man ! may Allah show you the right way !!

[anxhelanazeraj]

Thank you so much for all those videos, l found you channel at least 20 hours before and up to now l have seen more than 50 of them. Related to this one, l have a question on the first part of the proof.
At the part on 4:50 l not understanding why we can change the order of them.
Honesty too much appreciation.

[arbsieyasin]

Thank you so much, I got your lesson!

[sil]

Where do I find the one hour long video of examples for the first isomorphism theorem that you mention at the beginning of the video?

[하정훈-jj]

Is there another video of yours that explains why we need to check if the phi is surjective? 10:41

[aliakkari]

Plzz can you solve imo 2015 problem 2 😊

[enzoyu]

Thank you for the perfect logical proof.But in my opinion how to understand the theroy is more important.If we really understand what the theorem is really saying, the proof is just formal writing.So I really want to know how did mathematicians come up with this theorem and what does it really means.Thank you for your proof.And English is my second language, maybe I can't indicated well.So wish you can forgive and point out my mistakes.

[NecroMancer]

I thank you for the number theory course that you have raised the lessons well understood and explained, but I have a question for you can upload lessons on Legazander and Jacoby and the Eiler function and a squared residual with examples of questions on the subject?

[voorhees]

I think i have 2 questions

Did you ever tell why we got (H intersect N) normal to H for free by the last proof? If so, was it given in the end in terms of the kernel og phi?
I think i might be confused but isnt (H intersect N) normal to H because for every element q in (H intersect N), hqh^{-1} will be in H because it is essentially just a multiplication of elements in H?

When showing surjectivity of phi you write im(phi)=HN/N. Didnt we just show that HN/N is contained in im(phi) without the reverse inclusion?

Thank you so much for these videos, it has been my goal for some time to learn the theorems of isomorphisms for groups and your videos have really helped.