302.3B: Normal Subgroups

Examining normal subgroups, via their unwieldy original definition.

[fredseelig]

I love the fact that you speak quickly. You have a very direct way of teaching, and you always keep moving. You keepp me on the edge of my seat, ready for the next reveal. Big thanks for teaching this subject clearly and free of unnecessary mathematical jargon. You realize that there are only some times when you have to invoke the heavy machinery of formal mathematics. During an initial exposure, however, you do it right: Clear, direct, and LOTS of examples and counterexamples. I have loved every one of your abstract algebra videos. Many thanks to you!

[facejets]

You're a natural at teaching this stuff. Your inflection cuts hours off of people trying to decipher what a video's writers meant by listening to an actor playing a mathematician present it. That is, if they (me) ever figure it out at all.

[kirstens]

Your videos are very helpful - I appreciate the fast pace and quick speaking, since my brain works fast and it helps to always stay focused on what you're saying. It helps me to get to understanding the overall point/main idea sooner, and to hear about the relationships of those ideas to other ideas. If I need something repeated then I can just replay or pause it, and the fact that everything is written on the screen allows me to take screenshots to archive that I can easily refer to later on. Your points are very succinct and somehow you end up answering all the questions I didn't know I had, since you're able to say so much in so few words :) I also appreciate the examples, and snippets of extra information you add in. Super helpful overall!

[jessicapriscilacerqueiraba]

awesome explanation omg thank u so much, professor

[jozbornn]

Man, do I appreciate professionally-scripted, prompt review of these topics. It's a great change of pace from the hundred videos of people mumbling their way through the group axioms

[WinIsGod]

You are an excellent teacher, thank you for these videos.

[余淼-eb]

Prof. Salomone, your lectures are fantastic. Thanks so much for your sharing. Which text books do you recommend for your course?

[PunmasterSTP]

Man, the insanely high quality of these videos is definitely not...normal 😃

[MatthewSalomone]

No, there are nonabelian groups all of whose subgroups are normal. Example: Q the quaternion group

[hyperduality]

Left cosets are dual to right cosets synthesize normal subgroups -- the Hegelian dialectic.
"Always two there are" -- Yoda.

[Sarah-cqsd]

Thank you so much for the videos they are really helpful!

[GopinathShanmugam]

Hello Sir :-)
In group theory Normalizer and normal subgroup both are same?

[AnthonyCasadonte]

Ahhh interesting thought here in rewatching this video: firstly suppose we express something like a topological space but with groups in the form of a group's underlying set S and the group structure G together as (S, G) where G contains elements in S such that two elements are related by a binary operation (related in the sense of a relation that is associated) and such a xRb=c where a, b, and c are in S. And all the other aspects of a group are there. We can also consider for a set its normal

[ninosawbrzostowiecki]

Dude, I bet you're 28. Only a 28 year old could be this awesome!

[AnthonyCasadonte]

...subgroups, for example such a one H, as (S, H). But if G is simple I thought this is kind of like the trivial topology! Is there a name for a group with all of its subgroups being normal subgroups? (by this analogy would be perhaps like the discrete topology) Just a crazy thought hahaha

how did you get (13)(12)(34) ? You didnt wait . You wrote an answer without waiting. How did you do it quickly ? How did you do it? What is the practical way?

[AnthonyCasadonte]

Well any abelian group has only normal subgroups...hmmm does a group have to be abelian for all of its subgroups to be normal?

[noorameera]

At 3:41 how did you get (34)(14) = (143) ?

[fazedRR]

your explanations are so nicely expressed that it's a shame you speak so quickly!