Simple Groups - Abstract Algebra

Рет қаралды 127,559

Күн бұрын

Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order, alternating groups An (n bigger than 4), groups of Lie type, and the 26 sporadic groups, including the Monster Group.
Be sure to subscribe so you don't miss new lessons from Socratica:
bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
www.jmilne.org/math/CourseNote...
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : / socratica
► Make a one-time PayPal donation: www.paypal.me/socratica
► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9
Thank you!
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: / socraticastudios
Instagram: / socraticastudios
Twitter: / socratica
♦♦♦♦♦♦♦♦♦♦
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦

Пікірлер: 178

@bckzilla 6 жыл бұрын

Thank you for making KZfaq a better place to pass time.

@SalDin_ 6 жыл бұрын

literally have an abstract algebra exam tomorrow. videos are undoubtedly a great help!

@mksarav75 6 жыл бұрын

Thank you to the entire team who worked hard to produce this great video series.

@scipionedelferro 3 жыл бұрын

This is the most packed video of the series, content-wise. So many interesting and fascinating stuff mentioned, too quickly! It would be fantastic to have more videos on simple finite groups. You guys are the best!

@mortervolk6676 6 жыл бұрын

I can't believe you guys have covered so much info in less than 10 minutes! That's really great, Socratica. Keep up the good work. (From Syria with love!)

@eleazaralmazan4089 6 жыл бұрын

Thank you so much Socratica! You make mathematics very intriguing!

@janko4765 5 жыл бұрын

So, I am learning quantum mechanics and the abstract algebra is like a language you're using to talk about it. Although these lectures don't cover representations of groups and Lie's groups which are also needed for my quantum mechanics classes, I must say I'm in love! The concepts you're covering seem like they come in a natural way one after another and you want to know everything about every single concept. They don't seem just like a random topics you need to understand as fast as you can! The enthusiasm and the sort of an adventurous vibe I'm getting from the way you're talking is making me feel like I'm watching a movie! Thank you!!

@PunmasterSTP 3 жыл бұрын

That zooming-in and Monster group music! So suddenly intense, just like the rate of my learning after finding Socratica several days ago!

@raunitsingh676 2 жыл бұрын

I can only imagine how much time and effort and knowledge is required to put out a video like this.

@daca8395 6 жыл бұрын

"releace a video every hour" Nooo, I will witerally spand my life watching your videos...

@raunitsingh676 3 жыл бұрын

It's so sad that they have stopped making videos, now who will teach me more of such awesome things

@kennedyada1117 5 жыл бұрын

Man, I have an exam tomorrow and I was looking for slow easy to understand videos with examples that drive the points home, but you're just as fast as my lecturer assuming that I already knew everything about math when I was born.

@adeelali8417 4 жыл бұрын

This is where my journey with your series ends, you have been a great help! This video in particular is very comprehensive! :D Thank you thank you thank you!

@Socratica 4 жыл бұрын

We're so glad you found our videos helpful! Thank you so much for watching. Please share with anyone you think we could help! 💜🦉

@herbertpalines3443 3 жыл бұрын

This is a nice introduction to finite simple groups! Thank you, Socratica!

@arpanbhattacharjee470 5 жыл бұрын

Wonderful presentation!!! The videos are a great resource to understand the basics as well as some of the advanced concepts of Abstract Algebra neatly, quickly and efficiently... I'm a researcher in Applied Mathematics and the videos helped me a lot to revise my algebra concepts in a gist... Thanks a lot... Waiting for more topics on Advanced Mathematics to come...

@noellundstrom7447 6 жыл бұрын

I love seeing you go a little deeper into abstract algebra, nice job you earned a donation!

@Socratica 6 жыл бұрын

We're so glad you are enjoying our videos! Your donation is SO appreciated. It will help us make more of these videos!! Thanks so much for your kind words and support.

@Socratica 2 жыл бұрын

Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra

@kamyarghandi9995 5 жыл бұрын

Would love for this series to eventually get to an explanation of what E8 is and why it is considered such a beautiful mathematical object.

@rajendralekhwar4131 4 жыл бұрын

First of all thanks for your all videos.. I don’t get time to comment, on every video, but let me tel u , Your explanation is just awesome ..👍👍keep it up 👍👍 Please every time keep trying to make abstract mathematics as a layman language subject as long as possible I know it’s hard to do every time , but that’s the only way we can convert maximum individuals to love higher mathematics ...❤️

@CSAN33 6 жыл бұрын

These are actually really nice videos, I'm impressed!

@jaimelima2420 3 жыл бұрын

I am afraid to going to sleep today and have bad dreams because of this monster group. Thanks making us understand these concepts.

@gauravsinha6060 6 жыл бұрын

I love this channel. Thanks for the great video.

@luyombojonathan6688 5 ай бұрын

Thank you alot for these series

@ashwanirao7354 4 жыл бұрын

Your way of explanation is wonderful

@NH-zh8mp 2 жыл бұрын

Bravo, I love this video, it’s so fascinating and helpful

@My_oxytocin 2 жыл бұрын

Love your indetails information on group.❤️❤️❤️

@ruiyingwu893 6 жыл бұрын

I am pretty new at group theory, so I did some 'research' (aka me typing it onto Google ) ... |A_13|= 13!/2= 3 113 510 400 Thats... a lot of subscribers you are asking for...

@randomdude9135 4 жыл бұрын

T series has surpassed both pewds and Music to become no 1. But even they've got apprx 107M subs.

@jonmolina948 4 жыл бұрын

You could've simply taken the cardinality of S_13, 13!, and divided that by 2. The cardinality of even permutations in S_n is always the same as the number of odd (If n >= 2). You can prove it by defining a bijection between the two sets.

@kresimir1965 6 жыл бұрын

I got goosebumps when I saw Monster group :O And the music was whaaat

@Jung850 6 жыл бұрын

This is really awesome! Great work. 😍🤗🤗

@saurabhsingh-ow7ue 3 жыл бұрын

well this 8 mins video is the best investment of my life till now....thank you madam.....

@Socratica 3 жыл бұрын

That is so nice of you to say, thank you! We're so glad we could help. 💜🦉

@upendraagnihotri2686 3 жыл бұрын

Thanks for making me understand a bit in the ocean. I am struggling very hard to get the essence of it.

@moaadmaaroufiii2057 2 жыл бұрын

amazing work!! keep up

@priyanka-samal. Ай бұрын

Thank you in these 9 min video u explained a lot and in a simple way

@derciferreira2523 5 ай бұрын

You resumed 300 years of mathematics in just 8:52 minutes. Thank you.

@Grassmpl 2 жыл бұрын

This lady knows so much. How about a video on cohomology groups?

@christianorlandosilvaforer3451 5 жыл бұрын

wow at least i came to this video.. finally i can understand why pol eq. of 5 or more grade have not a general formula as solution!!! thank you socratica team!

@ChaudharyAteeq440 6 жыл бұрын

Great...Please upload more videos on abstract Algebra...also in linear algebra and real Analysis

@alvaroquispe-unsa 7 ай бұрын

Thanks for the video series, although I don't speal English, there are so useful for me. My best greetings from Arequipa - Peru

@AHeil1963 2 ай бұрын

There is a typo at 3:10: (N1/N2) should probably be (N2/N1). Congratulations and many thanks for the excellent video!

@gylje-9905 5 жыл бұрын

I am just amazed! I only can thank you..

@rodneytopor1846 5 ай бұрын

Nice summary. I think it would be helpful to elaborate the correspondence between prime numbers and simple groups as follows: Every finite group (positive integer) can be expressed as a product of a unique set of simple groups (prime numbers) by the Jordan-Hoelder Theorem (Fundamental Theorem of Arithmetic). But a given set of simple groups can be multiplied in different ways to give different product groups (the extension problem you mentioned), whereas a given set of prime numbers can be multiplied in only one way to give a unique composite number. I guess the reason for this is that arithmetic multiplication is commutative but group multiplication is not.

@noraalbogami586 6 жыл бұрын

unique presentation information ... thanks a lot ..

@anyachan567 4 жыл бұрын

Briliant work!

@guru6644 6 жыл бұрын

Very clear explain... Thanks.

@bobsagget9212 3 жыл бұрын

I study business but I really like these videos

@HikingWithRiley 5 жыл бұрын

Slide at 6:27, “intervertible” is written, “invertible” was spoken

@RalphDratman 6 жыл бұрын

This is a wonderful presentation -- thank you! What exactly is Socratica?

@Socratica 6 жыл бұрын

Thank you for your kind comment! We're a small team of educators who make videos for KZfaq! You can read more about us here: www.patreon.com/socratica

@michaelren4845 3 жыл бұрын

I cannot believe I have followed from episode 1 to 22 and intend to keep going. You explain these abstract and difficult ideas in a much clear way than my any of my professor. Thank you so much! [I might find a small typo in episode 22 for Simple Groups at 03:04 in the second line (title not included) "Quotient groups are simple: (N_1/1), (N_1/N_2), (N_3/N_2)..." Is it intended to be (N_2/N_1)?]

@huttarl Жыл бұрын

I wondered about that (N_1/N_2) as well. Glad it's not just me.

@vaishaliitkan7443 5 жыл бұрын

Nice explanation

@gharsepadhonasantoshkumarj9154 3 жыл бұрын

Great lecture

@mohdfarhan8562 6 жыл бұрын

Plz give video's on some examples on abstract algebra like inverse , order of an element..etc.

@woahdaggies 6 жыл бұрын

Please do a video on the Monster!

@sebastiananaya25 6 жыл бұрын

Hola Muy buenos videos, excelente calidad Me gustaría que volvieran en español

@davidpal1378 6 жыл бұрын

I like your videos on abstract algebra , but can you make videos on real sequences. Like bounced and unbound sequences , least upper bound greatest lower bound , infima , Suprema etc. if you do so then , It would be a great help .

@bat_man1089 Жыл бұрын

Thank you teacher 😊

@ahmedengineer5778 6 жыл бұрын

I like your enthusiam ..... you sure have passion for the subject you are discussing ..... but I think that you need to add more examples .... and more important real life applications ..... the problem that makes alot of people hate math is that they feel it is irrelivant to thier every day life ..... one of the merets of educational videos on youtube is the appility to show people how science really affects thier life

@heliumfrancium8403 Жыл бұрын

3 millions to watch abstract algebra is tough nowadays especially after the corona virus. Corona hit the education quality and will take time for that quality to recover.

@ladmondraxngfuskiii9426 6 жыл бұрын

视频讲的很清楚，获益匪浅！

@mohdfarhan8562 6 жыл бұрын

It's well undertaken video

@IjazKhan-fm4si 3 жыл бұрын

Great Socratica❤❤❤

@mueezadam8438 3 жыл бұрын

A masterclass presentation.

@information2949 6 жыл бұрын

Ma'am plz make one vedio on P group, sylow p-subgroups and related theorem

@fengzm 3 ай бұрын

|A13| is approximately 3 billion. Way to go, Socratica!😃

@eliasgarciaclaro6136 5 жыл бұрын

Este canal es increíblemente bueno

@chindinaresh7305 5 жыл бұрын

@manuelroman815 6 жыл бұрын

Muy buenos sus videos pero si colocan los subtitulos para que el publico en español pueda seguir disfrutando de sus videos seria genial!

@MarvellousMartha 4 жыл бұрын

you say "remember manifolds?" but i am not able to find a video of yours covering manifolds. which one is it? thx

@colaurier2594 6 жыл бұрын

Thanks a lot.

@FranFerioli 4 жыл бұрын

The gist of Galois theory in under 10 min! The groups might be simple, but this video is certainly not. Outstanding work, as usual Socratica...

@information2949 6 жыл бұрын

Thank you ma'am :)

@RurczakKurczak 2 жыл бұрын

3:04 can we take N1/N2, where N2 is bigger than N1? I think not, since N2 has to be a normal subgroup of N1 to be able to take a quotient group.

@giorapeniakov3153 2 жыл бұрын

seems like a mistake?

@thavibu 4 жыл бұрын

Interesting that two of the concepts in the video are named after 19th century Norwegian mathematicians, Abel and Lie

@basudebmondal954 2 жыл бұрын

Group is very interesting chapter in abstract algebra

@oldPrince22 2 жыл бұрын

To be honest, this video has a much higher requirements for the audience. Hence is not that consistent with the previous videos about abstract algebra. And the topics covered in this video is seldom used for a beginner of abstract algebra.

@spotlight9027 6 жыл бұрын

I need your lectures about real analysis and topology

@giorapeniakov3153 2 жыл бұрын

A factor group is also known as a quotient group

@cameronspalding9792 3 жыл бұрын

@8:23 The number she’s aiming for is half of 13 factorial which is 3.1 *10^9

@yenmejos3162 6 жыл бұрын

hi, can you also make videos about non-cyclic groups :)

@House_ssb 6 жыл бұрын

More about calculus please

@keepmoving5453 6 жыл бұрын

thank you so much mam (from India)

@mariojonaban1139 6 жыл бұрын

Nice!

@governmentday3511 5 жыл бұрын

thank you

@bhavyaanbarasan7919 4 жыл бұрын

Hi mam Can u please do a video on decomposition of graph

@filipve73 6 жыл бұрын

1) Time will tell ?? (abstract) Perhaps there is a group between the "Happy Family" and the "Pariahs" 2) For patreon support do you accept also Bitcoins ?

@Socratica 6 жыл бұрын

1) People are researching ways to unify the sporadic groups. I'll need to check on the latest research to see what progress has been made. 2) We *do* accept bitcoins! :) You can find our address on our "About" page: kzfaq.infoabout Thank you so much for considering supporting us!!

@aniketchandak7426 6 жыл бұрын

Please upload video on Riemann integral...

@algonte 6 жыл бұрын

Amazing...

@user-xs9oo9gc7u 3 жыл бұрын

I've heard that there is only ONE mathematician alive now who understands the whole 10000 pages of simple groups. S a d.

@dekippiesip 11 күн бұрын

And his name is?

@paramanandadas1319 4 жыл бұрын

At 3:05 there is a mistake. I think that is not N1/N2 but N2/N1

@Drtsaga 4 жыл бұрын

Hi guys! Can anyone explain how the monster group can contain quotient groups? I thought that in order for a group to contain a quotient groups, it needs to contain normal subgroups. (simple groups do not contain normal subgroups, and the monster is a simple group) Thank you.

@MuffinsAPlenty 4 жыл бұрын

@jamesshin4901 6 жыл бұрын

Great!!

@whalingwithishmael7751 5 жыл бұрын

Can you do a video on the monster group? John Conway thinks that he’s going to go to his grave without having learned why it’s there and that would be tragic

@alfredbeadman7114 2 жыл бұрын

Would love that. Want to learn more about it!

@bhiseahilya3632 Жыл бұрын

Unique!...🙏

@user-kw4er9un3e 3 ай бұрын

hello! why do we get R^(n^2) ? why is n^2 a dimension?

@mohitsaini2114 3 жыл бұрын

Nice

@himanshugarg6062 4 жыл бұрын

Stick to one of the names : like factor group or quotient group.. And similarly in other situations.. Maybe show an asterisk comment at the bottom of the video.. I'm a fan.. Trying to help..

@ashishpathak2947 6 ай бұрын

At 7:27 the instructor mentions that monster group contains 20/26 sporadic groups as either subgroups or quotient groups. But as monster group is a simple group, then it shouldn't have any normal subgroups right? And hence we shouldn't be able to form any quotient groups? Can someone please comment on what I'm missing here.

@MuffinsAPlenty 4 ай бұрын

I looked it up. Apparently the happy family are all _subquotients_ of the Monster Group. Given a group G, a group K is a _subquotient_ of G if K is isomorphic to a quotient of a subgroup of G. In other words, K is a subquotient of G if there is some subgroup H ≤ G and some normal subgroup N ⊴ H so that K ≅ H/N. This does not contradict the simplicity of the monster group because H will not be normal in G there. This is not a failure on your part, though, because the video didn't say this.

@himanshugarg6062 4 жыл бұрын

Is this connected to M theory in physics (because Monster group) and 26 dimensions that were needed before modern string theory allowed for 10 (before moving on to 11)..? P.S.: Very pop sciency.. I know..

@SSJProgramming 2 жыл бұрын

Great video, But slightly misleading at 5:14 There is no general formula for degree 5 and higher *** IF *** you consider only using BASIC operations like +,-,*,/, roots, powers, exp(x), log(x), sin(x), cos(x) etc. Its a common misunderstanding that this hold for ALL types of multivalued functions you can consider. And in fact, there are GENERAL solutions for degree 5 and higher. Using elliptic functions, or jacobi theta functions, some others I can't even recall, hypergeometric etc.