Why Normal Subgroups are Necessary for Quotient Groups

Proof that cosets are disjoint: • Proof: Cosets are Disj...
In order for a subgroup to create a quotient group (also known as factor group), it must be a normal subgroup. That means that when we conjugate an element in the subgroup, it stays in the subgroup. In this video, we explain why conjugation is so important to quotient groups!
Group Theory playlist: • Group Theory
0:00 Intro to quotient groups
5:10 Not all subgroups work!
8:28 Quotient group condition
12:15 Normal subgroup examples
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Music: OcularNebula - The Lopez

[@ezras7997]

Despite having less time to, thanks for still uploading.

[@stipendi2511]

I'm taking abstract algebra right now and all the videos on this topic were decent at best but this one was absolutely phenomenal!!! I finally feel like I made actual progress understanding the importance of normal subgroups. Thank you so much! One thing that would've been cool if you had covered is the equivalent definition of a normal subgroup that says that a subgroup is normal if and only if all the left and right cosets are equal
But either way, what a fantastic video!!

[@jrwarfare]

Great content. Wish I saw this when I took modern algebra.

[@Mateo-zd8mh]

Finally I find someone that explains where and why the idea of normal subgroups come from, thanks!!!

[@zeferreira8805]

Despite Socratica series about group theory being so good in general, i guess this topic was the one not so well explained, but thanks to you I finally understood the definition. Thanks :)

[@joetursi9573]

Great. Great ,great. You tell us in wonderful detail why a subgroup must be normal in a quotient group. I've never come cross what is clearly something that many students should question. The entire video is presented with clear, logical progression. Write a text,

[@ate..]

thx !! i was extremely close to a mental breakdown for not getting this at all but i do now x

[@albertyeung5787]

keep up your work, excellent

[@antoniofrancaib]

this is sooooooooo gooooood! thank you very much!!!!!

[@thecuriousjordan8193]

Nice video about normal subgroup.

[@tomkerruish2982]

Onward to the Finite Simple Group Classification Theorem!
Okay, okay, just show that A_5 is simple and so the general quintic can't be solved by radicals, and we'll call it good.
Seriously, man, keep up the good work. Here's hoping you can be on-campus next year.

[@Sarah-pu8un]

Great, thanks!

[@carlosraventosprieto2065]

amazing!

[@jaskiratchaudhary728]

Brilliant man

[@Ruvine_]

Great video

[@rakshithv4053]

Thanks man

[@alainrogez8485]

Brilliant

[@jabir5768]

OMG I have an exam in exactly a week on group theory, thanks for doing this !
(do some p sylows my dude if you can/want)

[@ScouseRobert]

Hi Mu Prime
I’m enjoying your group theory videos but the first five of them on your group theory playlist are marked as private.
Would it possible to make these available for all , as I would be interested to watch them?
Please keep the cool stuff coming. 👍🏻

[@MuPrimeMath]

All of the private videos are scheduled to release in the next two weeks!

[@ScouseRobert]

Thanks for the quick reply.
I mixed up the order the private videos are the last five in the list rather than the first five. 🤦🏻‍♂️
Something to look forward to.

[@lowerbound4803]

Cool!!

[@carloevelynf.9136]

💖💖💖

[@user-ud9ds8oc7e]

I’m Japanese. I’m watching to interest for video. Normal subgroup is difficult to learn for me. Show me more examples!!

[@MuPrimeMath]

In the next video, we will talk about how the kernel of a homomorphism is a normal subgroup!

[@user-ud9ds8oc7e]

@@MuPrimeMath thank you!!!