First Isomorphism Theorem for Groups Proof

[@branjara]

Good proof, but it would have made more sense to change notation. Instead of letting H=Ker why not let K=Ker? And K should in fact be the Image according to the theorem. After I reminded myself of what notation you were using it was a very good proof to follow.

[@chromosome24]

when psi took the coset back to k, i was like aaaw, but then when phi got onto, i was like NO SHE DIDN'T!

[@TheMathSorcerer]

Lol

[@SubhamKumar-eg1pw]

Great video.Can you please provide a video for 3rd theorem ?

[@jackliyong]

Excellent proof!

[@TheMathSorcerer]

+Yong Li thank you!!

[@superevilgoldfish]

Hi can you clarify the transformation you made on 4:38 ? you said "thats how you multiply cosets" and I've never seen that done in the course Im taking. I mean it sounds like you could only do that if you prove Commutative of Hx. Also if you have any free online book recommendations I would love to hear! Thanks!

[@GM-mh4ws]

Are x and y in claim 1. elements of G or H? I don't follow how Hx=Hy implies that xy^-1 is in H, unless x, y were elements of H to begin with, by the subgroup test.

[@TheMathSorcerer]

[@XxKathrynRyderxX]

amazing, so easy to understand! thank u!! (:

[@TheMathSorcerer]

You are welcome!

[@zhengyangfei5599]

Is well defined and injective the same thing?

[@raducumihaicristian]

When we state this theorem it shouldn't be that Im(K) ~~ G/Ker(phi) instead of K ~~ G/Ker(phi)?

[@jainamkhakhra3898]

Thank you so much!!!.

[@TheMathSorcerer]

np thanks for watching:)

[@quiveirojason]

Amazing. Nice presentation

[@TheMathSorcerer]

Jason Quiveiro thank you!!

[@ninosawbrzostowiecki1892]

I know this might be a stupid question, but why can we assume that phi is onto?

[@TheMathSorcerer]

+Ninosław Ciszewski it's part of the statement, note if we don't assume phi is onto, using a similar arguement, we can show ph(G) =~ G/kerPhi. However if we assume it's onto, that means phi(G) = K, so we can say K =~ G/kerPhi, and this says something about K which is more useful.

[@287MdSahil]

Thanks a LOT

[@josephtursi7529]

Nice!

[@TheMathSorcerer]

thx:)