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).
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 ?
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?
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.
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!
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 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?
