mam please yeh bta dein hum ek group se dosre group pr homomorphism kese define krte..... aur kb homomorphism exist krta (jese s3 se z6 pr homomorphism defined nhi kr sekhte kyun?)))) please must reply
Let G be group of order 4, which is not cyclic and let S3 denote the symmetric group on 3 letters. What is the number of group homomorphisms from G→S3 ?
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Your method fails in case of infinite groups: If we apply this algorithm to find number of homomorphisms from (Z,+) to (Z,+) then we get total of 3 homomorphisms but there are infinitely many homomorphism. How we get three from this algorithm: The normal subgroups of Z are {0}mZ and hence its quotient groups are Z/{0}≈Z and Z/mZ≈Zm Therefore we are in search of total subgroups in Z(in codomain) which are wither isomorphic to Z or finite cyclic subgroup of order m. Now the Z is subgroup of that and |AutZ|=2 and the only finite subgroup of Z is {0}≈Z1 and |Aut(Z1)|=1.Hence total number of group homomorphism is 2+1=3 But actually there are infinitely many homomorphisms as f:Z-Z defined by f(1)=n(f(1)) and 1 is generator
Assalam o Alaikum respected mam
Zabardast Ma Shaa Allah
Jazaki Allah khyran
May Allah gave you strength Ameen
please make videos on concept of normal subgroups, quotient group. it will help a lot. Also your videos are really very much benificial.
Where is its' next lecture. Please reply...
ua-cam.com/play/PLTchWiHrNniwBDWshXJ304Du_PO_ki50-.html&si=lIGzuC6tFaJ-4geP
Topic Wise playlist of Abstract Algebra
Thanks ma'am 👍👍
Amazing content
Amazing explanation
The most helpful video ever seen on group theory 😃thanku so much mam..... 🙌🙌🙌🙌
Di iska next lecture kha h
Wow you did it very smooth
Number of homomorphism ke liye thankQ, next time "Which are those homomorphism " iske bareme ek video banayiye.
Please ap kb se padhyege
Nice 👍😊
mam please yeh bta dein hum ek group se dosre group pr homomorphism kese define krte..... aur kb homomorphism exist krta (jese s3 se z6 pr homomorphism defined nhi kr sekhte kyun?)))) please must reply
Very good explanation
Homomorphic ki aur example k liya Viedo upload kijya plz
Very clear
Mam plz make video for homomorphism f: Dn - Dn
Mam vector calculus ke liye koi book suggest kijiye jo online available ho ske
Let G be group of order 4, which is not cyclic and let S3 denote the symmetric group on 3 letters. What is the number of group homomorphisms
from G→S3 ?
Nice explanation mam...thnk u so much
Ma'am normal subgroup kitna he ak group me ke se bar karu
🎉🎉🎉❤❤
Please send a link for :Just next video to this one....
News : I am beginning an Online Detailed Course (Paid) on Unacademy. For those who want to see the detailed course, and can afford it, should join it. 😇
Very nice explaination dii lagta h ki aap dubey sir ki student rhee hai😊
Mam please send me next video on homomorphism.
Mam,
f:S3-Z6
Then no of homorphism f(S3)=?
Yeh kaise karein?
Mam plz ans...🙏
Depends on Zm
If m is odd then ans is 1
If m is even then ans is 2
@@wasubhat4163 that's mean hare ans is 2, are u sure? In f(S3)?
@@SouravSir100 yes i will provide u link
@@wasubhat4163 ok.send me please🙏
Thanks Mam
thank u now i m more confused :)
Thanks ...
lGl=1 ko Z1 bolna achha nhi h identity jyada better h
Your method fails in case of infinite groups:
If we apply this algorithm to find number of homomorphisms from (Z,+) to (Z,+) then we get total of 3 homomorphisms but there are infinitely many homomorphism.
How we get three from this algorithm:
The normal subgroups of Z are {0}mZ and hence its quotient groups are Z/{0}≈Z and Z/mZ≈Zm
Therefore we are in search of total subgroups in Z(in codomain) which are wither isomorphic to Z or finite cyclic subgroup of order m.
Now the Z is subgroup of that and |AutZ|=2 and the only finite subgroup of Z is {0}≈Z1 and |Aut(Z1)|=1.Hence total number of group homomorphism is 2+1=3
But actually there are infinitely many homomorphisms as f:Z-Z defined by f(1)=n(f(1)) and 1 is generator
haii ishiska
ishq hi ho gaya tumse
love from BHU
Also solved by Trick 2 😅
So lengthy and boring
But Useful
सबकी फटती है...😂😂
Study video me aise language kaun use krta h...🤐🤐🤐🤐
@@pujadutta1426 yes you are ryt.
please make videos on concept of normal subgroups, quotient group. it will help a lot. Also your videos are really very much benificial.