Group Theory | Automorphism | Automorphism Examples & Theorems | Abstract Algebra

[@gajendrapurohit]

Thanks for your comment, your appreciation always motivate us to do such kind work. Join Telegram Channel : t.me/mathsbygpsir Instagram Handle : instagram.com/dr.gajendrapurohit/ Facebook Page : facebook.com/Dr-Gajendra-Purohit-453775988491992/ Unacademy : unacademy.com/@Dr-GajendraPurohit Link to B.Sc. Maths Playlist : bit.ly/34tTTdc Link to Engineering Maths Playlist : bit.ly/2OQ7Uvd Link to IIT-JAM Maths Playlist : bit.ly/2sh9pei Link to GATE (Engg.) Maths Playlist : bit.ly/35EAPct Link to IAS Optional Maths Playlist : bit.ly/2rwkOqj Link to CSIR NET Maths Playlist : bit.ly/2R8sUjV Link to Aptitude Playlist : bit.ly/3ewDR7z Link to Mathematical Physics Playlist : bit.ly/2NvRHLJ Link to Abstract Algebra Playlist : bit.ly/2A70LUb Link to General Aptitude For CSIR NET : bit.ly/2ZeWpma Follwing Topics are also Available 1. Differential Calculus : bit.ly/2OTYXB0 2. Integral Calculus : bit.ly/34rLA1R 3. Differential Equation : bit.ly/37IOlO1 4. Partial Differential Equation : bit.ly/2OM5iyA 5. Complex Analysis : bit.ly/2OP8hGp 6. Numerical Analysis : bit.ly/2QYVQuy 7. Integral Transform (Laplace, Fourier & Z-Transform) : bit.ly/37HRKg9 8. Statistics & Probability : bit.ly/2DmOt7Z 9. Operation Research : bit.ly/2pYYRjp 10. Matrices (Linear Algebra) : bit.ly/2OOBSzO 11. Fourier Series : bit.ly/34u7iC9 12. Vector Calculus : bit.ly/2qICwXO 13. Theory Of Equation : bit.ly/2XU9y33 14. Special Function & Series Solution : bit.ly/2XRSU4l 15. Infinite Series : bit.ly/37K6gUI 16. Group Theory : bit.ly/3ieUze2 Please share it with your Friends Thanks Dr.Gajendra Purohit

[@Blankpaper_openbook]

Sir, jab one one k baat Kar rahe the 3:48 par, toh apne bola domain( x1, x2) codomain(x'1, x'2) Mein domain k dono element codomain k x'2 Mein join ho gaye. But we know that In one to one or injective we can't have many to one. Isn't it?

[@ishikasharma6864]

It was a time when i possessed keen interest in mathematics but now i feel that opting maths in graduation is my biggest flex 😢 Its all on the basis of assumptions and theories... Missing the conceptual and calculating factor in maths now

[@simransaini4248]

Yeah same dude :( I'm also feeling low.

[@yuckertv2701]

It is called "PURE MATHEMATICS" for a reason 😅

[@Captain.Price33]

12 maths 🫡 Bsc maths🤢💀

[@evizgamer]

Its just about teachers, In schools teachers used to teach everything and every questions thoroughly but in most colleges and universities teachers doesn't pay much attention towards students. They just complete their lecture without any concern about students whether they understand anything or not.

[@thetransformer7023]

For those who do not understand try bhagwan singh vishwakarma sir ,he explains really well .like this comment to help others.

[@sumanverma864]

Sir apke videos se mujhe kafi help mili h.... Ap content bhi provide karte ho..... Thanks a lot

[@biharboardscience]

Thanks a million !!! Sir For English Language Suitable. 👌👌👌👌👌👌👌👌👌👌👌👌

[@gauravbohra6460]

i am grateful to you sir .........concepts are getting clear day by day after watching your videos ...thank you very much sir....

[@kartikdwivedi8073]

Tq sir . Your content is really helpful 💜💜

[@grradharadha4001]

Thank you sir for good teaching🙏🙏🙏

[@khadijashahbaz5159]

Thanks a lot sir❣

[@Aziz_acadmy_7]

Thanks Sir I understand this topic very well .....

[@chowdhurysadekanazrin2041]

Sir thank you for your outstanding explanation

[@physics-field1729]

Me vi video upload karta hu please play list me ja kar video watch Karo uske sathe me ekdam starting se upload kar Raha hu 3 lecture ho geya he please dekho Jo na samja aye please comment Karo me comment ka reply dunga

[@veersingh5662]

Best vdo for revision.

[@AbhinavKumar-yr6lp]

Thanks sir. Wait krna pada but final aa hi gyi

[@entertainmentforall6656]

Sir in Topic pr video bnaye Green function and Transform Method 1 Expansion of Green function 2 Transform Method 3 Closed form Green function Perturbation Techniques 1 Perturbation method for algebraic equation 2 Perturbation method for Differential equations Variational Methods 1 Euler Lagrange equation 2 Integrand involving one,two three and n variables . 3 Special cases of Euler Lagrange equation 4 Necessary conditions for existence of an ectremum of an functional. 5 Constrained maximum and minima.

[@charitylyngdoh8912]

Thank You soo much Sir🙏🙏

[@225__anukwary5]

Ur not like earlier anymore sir You were like very energetic teacher but now u teach very casual..

[@scholar-mj3om]

Marvelous💯💯

[@RP-gx7ds]

Thanku sir very helpfull Content.....

[@anjumfatima8550]

The set In(G) of all inner automarphism of a group G is a normal subgroup of atu(G)

[@creativestudy2020]

thanku so much sir this video is very helpful 🙏🙏🙏🙏🙏🙏

[@mdlelim4234]

Wonderful sir

[@Blankpaper_openbook]

Sir, jab one one ki baat Kar rahe the 3:48 par, toh apne bola domain( x1, x2) codomain(x'1, x'2) Mein domain k dono element codomain k x'2 Mein join ho gaye. But we know that In one to one or injective we can't have many to one. Isn't it?

[@physics-field1729]

Me vi video upload karta hu please play list me ja kar video watch Karo uske sathe me ekdam starting se upload kar Raha hu 3 lecture ho geya he please dekho Jo na samja aye please comment Karo me comment ka reply dunga

[@ayushkumarsingh2537]

Iska mean x1 and x2 two different elements na hokar 1 hi hai. Isliye hi one-one proof karne ke liye pehale f(x1)=f(x2) let karte hai and baad me ye dikhate hai ki x1 and x2 different nhi h balki x1=x2 hai. Isliye inki image same thi.

[@raj0442]

Thank you very much sir. Your videos are very helpful 🙏😊

[@samarthbadar786]

Sir plz make a video on transformation and permutation groups.🙏

[@tamilactorsstatus9503]

Nice 👍👍👍👍

[@The_Pi_Piper]

Sir I have one question.... Automorphism of Dn is isomorphic to which group ?? (Here Dn is dihedral group). I have only idea of its order.... Order of Aut(Dn) is n × phi(n).

[@UttamKumar-jz8oj]

Please sir yah sab Topics Covere keejiye inner automorphism, automorphism groups, automorphism groups of finite and infinite cyclic groups, applications of factor groups to automorphism groups, Characteristic subgroups, Commutator subgroup and its properties. (3 questions) UNIT - II Properties of external direct products, the group of units modulo n as an external direct product, internal direct products, Fundamental Theorem of finite abelian groups. (2 questions) UNIT - III Class equation and consequences, conjugacy in Sn, p-groups, Sylow’s 1st , 2nd and 3rd theorems. (2 questions

[@malayarana4397]

Thank you sir

[@chandansingingstage2028]

Sir inner automorphism banki hi rh gya aur kuchh special topic in group theory ex- conjugate , normalizer, center of group, Sylow theorem,

[@mohdriyaz1060]

Awesome and very nice video Sir

[@aashishgupta7496]

Thnx❤

[@43-nidhipandey81]

Thank you...sir🙏

[@AakankshaYouthsPower]

Very nice lacture sir

[@user-bm9fl2fj9j]

Sir we want a video on properties of isomorphism

[@mathsloversjn3453]

V nice explain sir

[@pramodprajapati9556]

Thanks sr ji

[@Rahul_Singha_1412]

Sir please make Videos on Direct Product of Groups 🙏🙏

[@abubakerjutt5052]

Thank u Sir ....but sir inner automorphism pr b ak detaild video upload kryn shukriya

[@dumeshmeher9291]

Nice 😊😊

[@chandankumargupta8174]

Sir upload a video on " abelianizing of a group And its universal property " My exam is on 6th January2022

[@Zpathan-fo8ym]

Thanx sir

[@Zpathan-fo8ym]

Sir differential geometry and manifold ke playlist bana diye. Pls

[@Chiraggupta_3005]

sir, How can I get the content pdf for revising?

[@nishaagrawal7311]

Sir please statistics per aur video upload kijiye mujhe apki sari video samajh me aati h please sir

[@Aziz_acadmy_7]

Respected sir : kindly share the endomorph ism topic ...

[@RahulMishra-xe9xm]

Mst sir ji love you

[@yuvrajvaish1836]

Let G be a group of integers under addition. Is the map f:G→G defined by f(x) = 2x, an automorphism of G?

[@ayushkumarsingh2537]

I think that it is not an automorphism. Because f(x) is not onto in this question.

[@ankitgoyal4415]

Wronskian equ p vido bnae

[@teerthendra]

Sir i have a question, homomorphism prove krte par jb hum (x1x2)^-1 ko kholte h toh x2^-1 pehle kyu aata hai or x1^-1 bad me ??

[@bushrahabib3391]

Sir is there any lecture on centralizer and normalizer ?

[@poojamangla871]

Sir complex analysis vale math prr bhi video uploaded krdo

[@himanibagri7217]

Sir , what is meaning of onto itself and into itself

[@himanibagri7217]

Plz reply sir

[@Ms_khatrifromhills]

Sir the last theorem you didn't explain it well 😔

[@mediaviper2957]

Yes sir

[@ayushkumarsingh2537]

Mujhe bhi nhi aa rha tha but maine basics padha tab aa gya😊

[@faizsiraj2489]

sir please upload lecture on conjugate subgroup,commutator subgroup

[@sachinjaiswal4600]

Sir ji main theorem are skiping you in this chapter so I request u pls explain this theorem because that's important points of exam

[@geepaspas3221]

sir , in the example 1 how do we understand it is to prove automorphism?

[@ayushkumarsingh2537]

Same doubt

[@kumkumkundu5324]

Please sir upload inner automorphism video

[@Aizal8080]

sir in following groups a) V4, b) (R,+) c) Zn d) U(n) e) Dn, f) Sn g) An h) Gl(n,F) i) Q8 j) group of order 15 j) group of order 25, Sir inky normal, automorphism and characteristics subgroups kaise find kr sakty hain short tricks se

[@muditshukla6780]

Sir how to integrate e^x^3 with limits 0 to 1

[@akhilmallah9858]

Sir msc pre ke liye abstract alzebra ke chapter ke bara me bataiye

[@RahulSahu-ot4yb]

Group me 4 property hoti h ap 3 hi bray ho sir .... closure kha gya

[@laveenalaveena6150]

In exam if they asked if G is an abelian group of o(n) were n is greater than two ST G has an element autom which is an inner automorphism den wat we hv write

[@sumanverma864]

14:38 smjh ni aya

[@dwimaitreeswain4754]

Plz sir Group action video share

[@bismayprakashlenka8655]

Why should we take gof sir on 12.07 minute

[@ayushkumarsingh2537]

To show closure property

[@vivekkumarjha9511]

Plzzzz upload permutation group

[@rameshchpanda5690]

Sir app kaunshi book se padhate ho.

[@kumkumkundu5324]

Sir inner automorphism video nehi hai kya??

[@Leotornato]

Centre of group bta dijiye gurudev

[@shreyas_n_life]

Where is Inner- external Automorphism sir?

[@waytowardssuccess207]

Sir thora slow samjhaye apki speed zyada h

[@ratneshsoni4431]

Sir 12:05 pe gof wala concept clear ni hua

[@ayushkumarsingh2537]

Agar two functions one-one and onto hai to unka composition bhi one-one and onto hota hai, aur ye sir closure property dikhane ke liye kar rhe hai.

[@nidanaaz7541]

Sir paper kbse start hoge BSC k m student of MJPRU University

[@abhishekmisra9375]

🙏🙏

[@yoyo-pd1by]

You speak very fastly...

[@physics-field1729]

Me vi video upload karta hu please play list me ja kar video watch Karo uske sathe me ekdam starting se upload kar Raha hu 3 lecture ho geya he please dekho Jo na samja aye please comment Karo me comment ka reply dunga

[@Leotornato]

Centre of group

[@arjunsinha8359]

Sir kisi group ka aut G kaise find krte hain?

[@physics-field1729]

Me vi video upload karta hu please play list me ja kar video watch Karo uske sathe me ekdam starting se upload kar Raha hu 3 lecture ho geya he please dekho Jo na samja aye please comment Karo me comment ka reply dunga Meine apka prblem update kya he kal Tak video ajayega

[@arjunsinha8359]

@@physics-field1729 ok

[@physics-field1729]

Tum comment karte rehne me upload karta rahunga

[@nidanaaz7541]

M 2 comment

[@attaulmustafa4283]

Outer and inner automorphism bhi beta dn

[@anjumfatima8550]

Sir meri ek question haa

[@santoshpinjari7]

✌✌✌✌

[@yogendrasinghnaruka4152]

Sir abhi bhi group theory ke questions solve nhi ho rhe h

[@yogendrasinghnaruka4152]

Saari videos dekhne or samjhne ke baad bhi

[@hemlatasharma6078]

Bhai yh hi haal hai.....mera bhi , jo yh kra rhe hai wo previous year ya assign m hai hi nhi.....

[@karansher9762]

sir thoda slow bola karo

[@agaadhr5394]

Play speed 0.25 kr lo

[@anjumfatima8550]

Confuse

[@shwetagautam3126]

Go slow sir

[@coolmind2476]

Please don't publish video with English titles if you don't talk in English. Its a scam.

[@rupalimohanty9920]

𝓣𝓺𝓼

[@muskansaini2342]

Sir in this chapters or in this Book there are so so so many theorem we understand them how we can learn all the theorem at the same time..... They all are like a little hard to learn 🥲🥲🥲

[@SawitriDevi]

Thanks Sir 👍🏻👍🏻

[@raj0442]

Thank you very much sir. Your videos are very helpful 🙏😊

[@Shivakshi-ze2jq]

Thank you so much sir

[@bishambuthyal56]

Thanku very much sir ❤️

[@NRUSINGHAPRASADMAHAPATRA]

Thanks sir 😊🙏🙏

[@prabhabhatt4541]

Thank you sir ji

[@Leotornato]

Centre of group

[@bapin5887]

Thank you so much sir

[@abhishekprajapat5305]

Thanks sir 😊

[@harshruhela7321]

Thank you Sir

[@mamtatripathi6876]

Thanks sir 🙏

[@mantashaahmed6478]

Thanks 😊