Simple Groups - Abstract Algebra

[@bckzilla]

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

[@SalDin_]

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

[@mksarav75]

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

[@mortervolk6676]

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!)

[@scipionedelferro]

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!

[@PunmasterSTP]

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

[@raunitsingh676]

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

[@raunitsingh676]

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

[@kennedyada1117]

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.

[@eleazaralmazan4089]

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

[@adeelali8417]

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]

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

[@daca8395]

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

[@janko4765]

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!!

[@jaimelima2420]

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

[@kamyarghandi9995]

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]

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 ...❤️

[@herbertpalines3443]

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

[@derciferreira2523]

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

[@noellundstrom7447]

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

[@Socratica]

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.

[@arpanbhattacharjee470]

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...

[@rodneytopor1846]

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.

[@Grassmpl]

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

[@michaelren4845]

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]

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

[@ruiyingwu893]

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]

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

[@jonmolina948]

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.

[@RalphDratman]

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

[@Socratica]

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

[@HikingWithRiley]

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

[@saurabhsingh-ow7ue]

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

[@Socratica]

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

[@ashwanirao7354]

Your way of explanation is wonderful

[@AHeil1963]

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

[@kresimir1965]

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

[@priyanka-samal.]

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

[@ahmedengineer5778]

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

[@bobsagget9212]

I study business but I really like these videos

[@alvaroquispe-unsa]

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

[@upendraagnihotri2686]

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

[@luyombojonathan6688]

Thank you alot for these series

[@cameronspalding9792]

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

[@My_oxytocin]

Love your indetails information on group.❤️❤️❤️

[@christianorlandosilvaforer3451]

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!

[@RurczakKurczak]

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]

seems like a mistake?

[@filipve73]

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]

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: kzbin.infoabout Thank you so much for considering supporting us!!

[@FranFerioli]

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...

[@oldPrince22]

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.

[@NH-zh8mp]

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

[@fengzm]

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

[@ChaudharyAteeq440]

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

[@paramanandadas1319]

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

[@davidpal1378]

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 .

[@ChanawerebiChanawerebi]

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

[@gauravsinha6060]

I love this channel. Thanks for the great video.

[@SSJProgramming]

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.

[@CSAN33]

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

[@woahdaggies]

Please do a video on the Monster!

[@moaadmaaroufiii2057]

amazing work!! keep up

[@gharsepadhonasantoshkumarj9154]

Great lecture

[@himanshugarg6062]

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..

[@bat_man1089]

Thank you teacher 😊

[@gylje-9905]

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

[@孙林可]

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

[@dekippiesip]

And his name is?

[@mohdfarhan8562]

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

[@Socratica]

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

[@himanshugarg6062]

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]

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]

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.

[@Jung850]

This is really awesome! Great work. 😍🤗🤗

[@mueezadam8438]

A masterclass presentation.

[@basudebmondal954]

Group is very interesting chapter in abstract algebra

[@guru6644]

Very clear explain... Thanks.

[@noraalbogami586]

unique presentation information ... thanks a lot ..

[@vaishaliitkan7443]

Nice explanation

[@MarvellousMartha]

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

[@sebastiananaya25]

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

[@thavibu]

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

[@whalingwithishmael7751]

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]

Would love that. Want to learn more about it!

[@anyachan567]

Briliant work!

[@tharagleb]

Order of A13 is 3,113,510,400

[@rylieweaver1516]

At 1:01, it should say that N is normal if gNg^-1 is a subset of N, not equal

[@MuffinsAPlenty]

Let G be a group and N be a subgroup of G. 1) gNg^-1 is a subset of N for all g in G 2) gNg^-1 = N for all g in G Statements 1 and 2 are equivalent. So either can be used as the definition.

[@rylieweaver1516]

@@MuffinsAPlenty How do you know that the statements are equal?

[@MuffinsAPlenty]

@@rylieweaver1516 You can prove it! Statement 2 implies statement 1 without really any work. So most of the work goes into showing statement 1 implies statement 2. So suppose statement 1 is true: gNg^-1 is a subset of N for all g in G. Now fix an arbitrary g in G, and we will want to prove that gNg^-1 = N. To show two sets are equal, we can show they are subsets of each other. By statement 1 (which we are assuming), gNg^-1 is a subset of N. So all we have to do is show that N is a subset of gNg^-1. To do that, we should take an arbitrary element n of N. We want to find an element m of N so that n = gmg^-1. Can we do this? I think this is a good exercise for you to try on your own, but you are welcome to comment back again asking for the rest of the details, and I can provide them.

[@IjazKhan-fm4si]

Great Socratica❤❤❤

[@AkiraNakamoto]

3:05 There is a typo/error. N2/N1, not N1/N2. The latter doesn't make sense.

[@Drtsaga]

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]

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.

[@qaziarshad939]

Hausdorff Space and T2 space is also T3 space ? is it Right?

[@ladmondraxngfuskiii9426]

视频讲的很清楚，获益匪浅！

[@eliasgarciaclaro6136]

Este canal es increíblemente bueno

[@chindinaresh7305]

Vf

[@mohdfarhan8562]

It's well undertaken video

[@MrMojo0417]

Let H be a subgroup of G. You can make cosets of any H within G. But cosets only quality as factor groups if H = N. Is this correct?

[@MrMojo0417]

This video was packed with information!

[@information2949]

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

[@Henry-yr2hn]

A13 is a huge group !

[@spotlight9027]

I need your lectures about real analysis and topology

[@giorapeniakov3153]

A factor group is also known as a quotient group

[@aniketchandak7426]

Please upload video on Riemann integral...

[@christopherrippel2958]

I was watching your videos in December to prepare myself for my Abstract Algebra course that started in early January. I come to find out that he is one of the few professors that started the course with category theory and threw me for a loop. Is there any channel on You Tube that you would recommend to supplement my studies?

[@mohitsaini2114]

Nice

[@1337w0n]

7:33 How is it that the monster group contains any of the other members of the happy family as quotient groups? I'm under the impression that simple groups can't have quotient groups.

[@MuffinsAPlenty]

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.

[@mehdinadjafikhah7314]

S_n is not simple for any n>1 because A_n is a normal subgroup with index 2 of it! But, A_n is simple for n>4.

[@AzrgExplorers]

Wait, how can the monster group have quotients if it's simple? Don't quotient groups and normal subgroups go together?

[@governmentday3511]

thank you

[@House_ssb]

More about calculus please

[@bhavyaanbarasan7919]

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

[@muhammadafzaalkhan9277]

at which author of abstract algebra book i select for himself to read.

[@manuelroman815]

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

[@yenmejos3162]

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

[@nowornever5598]

Thanks