Visual Group Theory, Lecture 5.6: The Sylow theorems

[@chilling00000]

This is by far the best lecture on Sylow theorems one can find on youtube.

[@yusufnzm]

This video is by far the clearest group theory lecture I watched. It was so good that some ideas really clicked with me for the first time.

[@zhuler]

in 31:05 it's easy to prove that conjugation of a p-subgroup is also a p-subgroup, so the only orbit is not bigger than np but equal to np

[@saquibmohammad2860]

Thank you so much professor. I was stuck on this for last three days

[@letslearnsomething0001]

Army

[@jtpmath]

I was stuck for the last 7 years. Ha!

[@hritizgogoi3739]

Thank you Professor for these amazing lectures

[@anmolbhanot5350]

Thankyou so much for these lectures !!! The way you teach with intuition & understanding is of great help ☺

[@余淼-e8b]

Amazing videos. Thank you, professor.

[@maru3295]

Thank you very much sir! I am currently reviewing about Sylow Theorems and this video helped a lot.

[@AxiomTutor]

Good pictures, clear explanation--very nicely done.

[@BSplitt]

I believe there's a small notational error at 25:06. I think it should be [G:H] instead of [G,H].

[@popoubc]

Thank you for such an amazing presentation of this powerful result!

[@alexandergrothendieck1571]

Merci beaucoup et super travail.

[@hinyikiwilemithi4855]

Thank you so much. This video was very helpful. I wish you were my lecturer

[@dananifadov7261]

hey! in 11:20 - I wanted to ask in what video do you prove that the order or the quotient group - normalizer of H mod H is a multiple of p? hanks a lot for this video!

[@ProfessorMacauley]

The previous one, on p-groups

[@kyleyan5974]

oh my gosh ,why you so great ! I love you!!!You are the one who teach it really easy.I can't agree more!🥳🥳🥳

[@pobodjjd]

Really Helpful with graphs!Thank a lot!

[@santosinibiswal6853]

It's really very helpful sir...thank you

[@Jd-dw8rn]

Thank you very much for these great videos ! Just a small remark: at 18:40, when you say "each of these subgroups contains a nested chain of p-subgroups", we did not yet prove that there is only one chain (if this is even the case) - couldn't there be a lattice of p-subgroups instead of a chain ? Although the proof only shows how to build one such subgroups, couldn't other methods yield distinct p-subgroups ?

[@Democritus477]

Thanks for the very helpful videos. I wanted to let you know that Sylow's name is not pronounced See-low, it is pronounced similarly to Sue-loav (as in loaves).

[@boranerol750]

Hi, To be fully rigorous, wouldn't you also want to show that H' is a subgroup in your proof od the first Sylow Theorem? If this is obvious, how do you see it?

[@igna02]

H' is constructed as the preimage of under the quotient. Then use that the quotient is a group homomorphism and the preimage of a subgroup must be a subgroup.

[@truong62]

Nice Sylow theorems explanation. Have we the proof of the such normalize group Ng(H) existence ?

[@rasraster]

Pretty amazing stuff

[@tianqilong8366]

The best!

[@samwalters3824]

amazing

[@fsaldan1]

Does the reasoning behind the normality of P5 generalize? That is, if G contains a subgroup H that is not isomorphic to any other subgroup of G can we conclude that H is normal?

[@ProfessorMacauley]

Yes! Because in that case, xHx^{-1} must be equal to H, for any x.

[@ilusoeseconomicas2371]

@@ProfessorMacauley Thanks. And also thanks for the great videos. The explanations are clear as crystal. Only a few videos about Advanced Linear Algebra? I am waiting for more. And what about Lie Groups and Representation Theory, two other very interesting topics?

[@okweonahi6781]

wow!, very awesome.

[@ourdreams823]

thank you

[@leewilliam3417]

Mmmmm❤

[@wesleysuen4140]

/ˈsyːlɔv/ 😎