Cosets and Lagrange's Theorem Part 3

[@ibtissamarbib-krasta6955]

this is outstanding ... straight to the point, very visual, and great pedagogy ...

[@nathanaelspiteri4788]

honestly after 2yrs of studying Group theory, I'm finally understanding 10x to this playlist

[@naru909]

Thank you so much. I was stressed to the max because of this subject but now I am starting to understand!! Very well made videos. Thanks for sharing.

[@andrewcenteno3462]

Phenomenal explanation

[@josephochemen9599]

Wow, this videos are great. They are really opening my understanding on group theory.

[@michaelwoodhams7866]

Instead of introducing normal subgroups as this weird thing, and then proving this aH=Ha theorem, I think I'd have approached it as "Wouldn't it be neat if aH=Ha? What would have to be true to make this work?" I.e. use this theorem as the motivation to define "normal subgroup".

[@johncoates1923]

Just discovered this!
Thank you, you have a rare talent for making hard things easier. I look forward to view other Group Theory videos you've made.
Your range of topics is most impressive! Are you a medical doctor or pharmacy researcher?
Excellent work!

[@ricegoing]

So well explained!!!

[@AryaDhayal]

thank-you 😇

[@mritunjayy]

okey! right!

[@absolutezero6190]

I love that

[@vojta6734]

Thank you very much, exactly what I needed

[@briannewman9285]

Can you explain how you went from "try" to "is"? I understand why aha' is in H, but I don't see where you proved it is equal to h'

[@debendragurung3033]

IF H is a abelian Subgroup of some nonabelain Group G, are the coset generated by a in G , aH (or Ha) abelian?

[@elliotnicholson5117]

No. You can disprove that with a counterexample. Take the non-abelian group s3.

[@debendragurung3033]

Oh yes i see. for H={i,c,c2} and a= t12 not in H, the composition aH={t12,t13,t23} which of course isnt abelian.
Sweet

[@christopherrosson2400]

Okay, I don't understand that first proof