Group Theory | Isomorphism | Examples of Isomorphism

[@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

[@thewarrior2123]

Sir your vedios are very helpful for us please keep continue

[@rahulnamanverma4445]

DHANYAWAAD GURUJI

[@ujjwalyadav8780]

Thanks sir u had covered approx complete algebra🔥🔥

[@missionDC]

Thankyou sir... Please sir it's request to you complete the abstract algebra book because my exam is on 8 April... Your videos help me a lot

[@pragathiyp5622]

fast as well as skipping things without explaining in a few examples

[@riyakashyap3261]

Exactly

[@visheshyadav6190]

​@@riyakashyap3261 +1

[@mathlover9248]

sir I like u teaching... Really ur lectures r very much useful for me

[@saniyamalik6718]

In 3rd example, hiw are the tables identical?

[@saurabhsuman7417]

Tables are identical in the way that if you replace the respective mapping then you get the same table

[@tusharbagal2432]

Very Helpful and Nice video. Your teaching is very good sir. Thank you so much

[@gurubasavagurubasava5292]

Thank sir for the vedios on msc entrence exam parpose

[@tanjinaaktar1146]

Thanks for giving us most most clearly class

[@prashantsinghps2779]

apka content bahut helpful hai

[@paridhisharma3896]

Thank you sir, it is very helpful for me

[@Ankitkumar-tt2zz]

Thak you very much sir for providing such a well compiled content.can you bring a series of questions of IIT jam level with their solution with tricks???

[@lol-ts6ne]

Sir, literally..... Big fan of ur explanation... Keep it up... Thnqq sir

[@Manu-rm9uj]

itne chante bharoga

[@manansharma7108]

Sir example 3 (b) if we are replacing the numbers we are not getting the identical table .. so sir how it is isomorphism

[@jinalhere]

Confusion 🤧

[@manansharma7108]

@@jinalhere It's not an example of isomorphism🤘

[@rashmikumari5380]

Exactly

[@ayushkumarsingh2537]

Same doubt

[@AjayKumar-gr1mq]

Thanks for making videos of this topic 🙏

[@MLNiharika]

We love you sir.

[@sujitkumarmeher4958]

Sir example 3 (b) how table are identical

[@Rakeshkumar-jf4ty]

Humko bhi samjh nhi aaya...

[@ayushkumarsingh2537]

Same doubt

[@rajuverma4540]

14:18
Sir according to the table you made the functions are not matching
f(0) is not replacable by 1

[@jacksonmichael3481]

I saw this too.

[@manjupoonia7180]

Thank you so much sir your class very helpful

[@abhinandanjain2399]

Thank you so much sir 🙏

[@jyotisekharpanda9368]

It's very nice sir .your all videos are very helpful .. but your teaching way is little bit speed .

[@faizajavedgani8030]

Sir solve this question
Let m and n be positive integers such that m/n
Prove that the map fhai:z/nz implies that z/mz sending fhai (a+nz)=a+mz for any a belong to z is a group isomorphism

[@Mridulmishra06]

V.nice explaination sir

[@acousticm.j.8466]

sir example 2 thoda confusing raha starting kyunki aapne uski mapping question ki jagah answer me di🤔🤔🤔🤔🤔🤔🤔

[@hearthacker5565]

Ap sahi ho .. apka confusion genuine hae

[@rakhisingh6441]

Sir u r the best👍👍👍🏆🏆🏆. Thank u sir🙂🙂

[@scholar-mj3om]

Marvelous💯💯

[@gentlemen423]

Back to back lecture jai ho

[@arpandas8708]

You are a excellent teacher sir but plzz try to talk slowly

[@ppp2330]

thanks a lot sir...can u slow a little bit...it might help more

[@MubashirKhan-ki5qo]

Kindly make lecture on commutator subgroup. Theorem commutator subgroup is normal subgroup of G..

[@rahulnamanverma4445]

JAI SIYARAM JAI HANUMAN JI

[@hsrada433]

Nice lecture!

[@raghavvarma6060]

Sir, eg 3 is not an insomorphism. f does not preserve composition. I have checked it multiple times. Please do check from your side and rectify the error if any.

[@ayushkumarsingh2537]

eg 3(b)

[@pirooo6544]

ye example a,b,c me morphism morphism karta gaya pir example 1 me homomorphism??

[@pranjal7348]

Sir please upload vedio on permutation soon I have exam on Monday and 2 units with permutation also remain

[@PriyanshuKumar-mt4zf]

video ka spelling ata ha

[@pranjal7348]

@@PriyanshuKumar-mt4zf dekh it's an educational channel otherwise the the reply will be just like that you will never ask someone for their spelling error

[@nileshyadav9173]

Sir can you aload the next video on isomorphic till evening becouse tomorrow will be exam

[@thewarrior2123]

Your vedios are very helpful

[@pawan6373]

Arre sir screen shot bhi lene diya kariye thora solve krke samne khade ho jate h phir turnt slid skip lr dete hai 🙄

[@arnavlearningandgamingchan7630]

Thankyou sir 🌺😊

[@learnalways8213]

Sir please tell how it is onto in R negative numbers are also there

[@zainabcheema4948]

Sr its amazing

[@chemphyianschool6727]

Thanks sir great

[@saurabhnarain144]

Pranaam guruji

[@Arkwith0]

आपका बहुत बहुत आभार सर 😍😍😍

[@themathmotivor.]

Good sir keep up it
Allah apko ajar dy

[@utkarsh_108]

ajar ky hota h bhai

[@themathmotivor.]

@@utkarsh_108 apko sumj nhi ani

[@utkarsh_108]

@@themathmotivor. chalo thik h fir

[@geethaaliyangal5147]

thank you so much sir for the classes. in example C how is it becoming onto? logx is always positive , right ? so F(R+) contained only positive part right

[@princeraj2750]

log x can be negative as well as zero. eg.- log(1/2), log (0.4),etc.
value of x in logx is always +ve.

[@geethaaliyangal5147]

@@princeraj2750 Thank you so much. I googled and found it. Iam restarting studying aftera long gap. So some points are lost

[@srijit009]

nice concept ❤️❤️

[@mayank_singh_43]

sir in example C at 6 min 50sec time , Negative numbers of R doesnot have it's pre-Image present in R+ , So how it became onto?

[@jacksonmichael3481]

e^x > 0 always. So for any +ve ans -ve values of x ie R, it produces only real numbers greater than 0.

[@dineshkumar-pl3ix]

sir lekin ye kaise pata chalega ki mapping kya lenge

[@sangeethagupta8985]

Sir upload video on ring , subring plzz

[@alphaa23]

Sir please upload video on normalizer and centralizer

[@vikaskumartiwari5513]

Nice explanation ❤️❤️

[@saipuja7989]

Sir, in 14:50 , hum kya likhe? , 1,2,3,4 ko replace karen ya 1,2,4,3 ko replace karein? Plz bataiye sir

[@lonelyburger9069]

Yeah.... 1 2 3 4 likh lo... Lkin agr 1 2 4 3b likh lo tw koi msla Nahiii

[@dalitshiv834]

Sassy B+ich🐩🐕

[@akash4298]

Table 1,4,2,3 hoga

[@rohitraghav7699]

Sir, Riemann integration pe vedio kb aenge.

[@anjaleemaurya1180]

Abstract algebra is related to all videos very helpful.
This video is matching of Allahabad University syllabus .In present time is all College teachers is not teach to perfect online classes. So sir is smart and easy language teaching for me very,..........,... helpful.

[@sunny-uh3wg]

sir...Real Analysis apki playlist me nahi mil rha hai. plz help me.

[@mathsloversjn3453]

V nice explain sir

[@deepakKumar-pb6pt]

Very nice Sir

[@AbhishekMishra-kv1ih]

Sir permutation wala topic jaldi dal doo 18 march ko paper haiii

[@MuhammadAslam-cw5mj]

Love ❤️ dear sir

[@fahadansari9387]

thank you sir

[@funnymathematics]

Thanku sir ❤️

[@mohammednaeemlodhi8507]

Sir please upload permutation group also

[@Rakeshkumar-jf4ty]

Example 3b m table 2 kaise form kiye ye samjh nhi aaya sir? 🤔 🤔 🤔 🤔

[@dipalichakrawarti6847]

Thanks sir!!!!

[@shubhammaths4761]

Thanks sir

[@Rahul-vl1no]

Sir you did blunder in 2nd example...correct that...please show the right way to solve

[@harisqureshi4792]

Sir please iit jam 2020 paper solve kijiye

[@kumarpradeep6569]

Sir please solve the following question it is very necessory.
if ψ be an isomorphism of a field F1 onto a field F2 such that α ψ = α' for every α ∈ F1 then prove that there is an isomorphism ∅ of F1 [X] on to F2 [t] with the property α∅ = αψ = α' for each α ∈ F1. do something sir .

[@pawanswami7656]

Nice
Please solve ∇2r^nr=n(n+3)r^n-2r

[@shradhashukla1562]

Sir please make on Fermat's theorem and eulers theorem

[@sejaljain9053]

example 3 m multiplication modulo ki table glt nhi h ky??????????

[@Mostokhokuwa]

sir eample2 mein apne not equal dikhaya too wo one one kaise hwa? plz answer dijia

[@TechMarcell]

Thanks🙏🙇🙏💕 Sir

[@virenderendlliya1146]

Nice very nice sir

[@PinkMoonMHTV]

Hi sir can i have a soft copy of your powerpoint? Thanks

[@muhammadkashifshabbirahmed8361]

You teach well sir along with your speed well😏
Please teach us a bit slow🙄

[@bikrambose2783]

Thanks sir💖💖

[@kumarpradeep6569]

Also solve another problem sir.
let f be a field of characteristic o. then prove that a polynomial f(x) belongs f(x) is solvable by radicals over f if and only if its splitting field k over f has solvable galois group g[k,f].

[@Leotornato]

Centre of group ka video bnaaiye

[@jitendrasing3006]

Your explanation good but explaining fast

[@rahulkrishnvanshi3836]

Sir ek book meisomorphism ke definition me into aur onto dono likhe h kyu?
Only onto hota to into vaise bhi ho jata h dono likha h book me kyu?
Sir isi ko explain kr dijiye

[@avijitbarman2047]

{0}×R isomorphic to R. How it's happened.

[@AbrarAhmed-rs9zb]

Sir, is Z4 and A4 are isomorphism?? Plz help me,

[@Vector_Space_Iconic]

Nahi O(Z4)=4 but O(A4)=12

[@utkarsh3770]

Sir example 3 ka b part mein difference aa rhaa hai, aapne bas keh diya ki ho jaayega par ho nahi rhaa hai, please misguide na kariye, aur aapne uss table mein order bhi change kar diya hai jo nahi hota hai

[@themathmotivor.]

Sir one request
You speak to much fast some concepts we don't understand ur fast speaking
Plz deliver lecture in slow speed

[@theindoledge5833]

To Bhai speed slow kr lo na...

[@themathmotivor.]

@@theindoledge5833 ap meri behn kb sy hoi mery abu na ap ki ami sy merriage tu nhi ki ha

[@Manu-rm9uj]

you engliss too bad

[@Manu-rm9uj]

abe bsdk

[@Tushar-fh6qz]

permutation group ka question q dal dia... vo to baad me cover hoga

[@shehzadrasool4863]

Good but Sir jiiiiiiiiiiii what is this jesa k hmmm janty hen ye hota hy wo hota agr we know about this pehly c hi too yahan q aty?? Just slide too read na kia kren

[@rinkigupta5749]

Sir multiple choice questions chahiye

[@theindoledge5833]

Centum le lo... Usme mil jayenge..

[@SubrataGhanty]

1:56
Condition(1)
Last m ∀a,b∈G hoga
...may be typing mistake 😊

[@HackYourGrad]

Guruji 2 example me ek doubt h
Real number bola h lekin e real nahi h
Plzz ............

[@Vector_Space_Iconic]

e real nahi hai😅 Imagination se bahar aao

[@W__Edits]

love you from Pakistan

[@cvraman5908]

Well

[@ummehabeeba5397]

Sir mapping kesy ly gy

[@penancepoint4589]

❤

[@ayaitchgaming]

8:20 why

[@SiddlovesIT]

Are sir😂aram aram se padha lo palwal 😂 nhi nikalna h😅

[@Satya_deep]

Question 3(b) is wrong

[@theindoledge5833]

I have also doubt

[@jyotipurba3513]

Ya exactly...i have also doubt in that question..i thought i was wrong 😂😂😂

[@ayushkumarsingh2537]

Same doubt

[@anuradhasaha7668]

OP SIR OP