Sir, At 20:08, the number of cycle decompositions of whose lcm is 4 and sum is 8 in S8 will be: 1,1,1,1,4 of type (abcd) , 1,1,2,4 of type (ab)(cdef), 2,2,4 of type (ab)(cd)(efgh), 4,4 of type (abcd)(efgh). You left the possiblity of type (ab)(cd)(efgh) ?. I don't know if i'm wrong or right. Please correct me sir.
@@MathematicalScience No sir. At, 20:08 we were finding, number of cyclic subgroup of order 4 in S8. So we're calculating, number of elements of order 4 in S8. So will there be four CD's which I mentioned above?.
Sir H1={0} agar generator h z8 mein to ye bhi to group ke Sare elements generate Kar sakta h na jese 0+1,0+2.... Hum use sirf trivial subgroup kyo keh rhe h please clear this doubt
Sir in the 2nd example in case 3,, you said it will be isomorphic to Z4,, but it will be isomorphic to K4 as well??? So basically we have to find number of subgroup isomorphic to K4 in S8 as well???
@13.36 time, how z8/(0) is isomorphic to z8 ? why can't it be isomorphic to non abelian group D4 or Q8 which has 8 elements? Q8 is quarternian group, D4 is dihedral group
@@ravishkumar8422 z8/(e) ~z8 always Because quotient group of z8/(e) contains all the right or left cosets of z8 a(e) type ke elements where (a) belong to z8. Now take a=1, 2,3,4... And form quotient group z8/(e)
@@MathematicalScience automorphism including both one one and onto I just want to count onto and there may be possibility s.t. some homomorphism are onto not one one so that such type of homomorphism are also included.
Sir u are my favourite teacher in absteact algebra .u r not only a good teacher but also a good human being
Outstanding mind blowing superb teaching and i have no words for your teaching method
Thanks sir for such a great and helpful video.
Ur videos r vry helpful sir 🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻
Sir 8:13 par Z2 SE k1 automorphism kese hua automorphism to group to itself hota h na? Aur Autz2=U(2) kese hua?
Nice explanation sir thanks for help us
21:47 aapne Likha h f(z8)=z4 but f(z8) isomorphic to z4 Hona chahiye na, ye equal thodi hoga?
Sir, At 20:08, the number of cycle decompositions of whose lcm is 4 and sum is 8 in S8 will be:
1,1,1,1,4 of type (abcd) ,
1,1,2,4 of type (ab)(cdef),
2,2,4 of type (ab)(cd)(efgh),
4,4 of type (abcd)(efgh).
You left the possiblity of type (ab)(cd)(efgh) ?. I don't know if i'm wrong or right. Please correct me sir.
but we need an element of order 8, there is no possibility being order 8
@@MathematicalScience No sir. At, 20:08 we were finding, number of cyclic subgroup of order 4 in S8. So we're calculating, number of elements of order 4 in S8. So will there be four CD's which I mentioned above?.
@@kirankumarsv4411 yes u r ryt,, very good ,, we must take this possibility
@13.36 time, how z8/(0) is isomorphic to z8 ? why can't it be isomorphic to non abelian group D4 which has 8 elements?
Can you plz let me know the any book which contains example and exercise like this..thanks
Nice sir
outstanding 💕
Thank you dear
Sir please upload such detailed videos on ring homomorphism. And thank you so much sir
29:00 par hum keh the h S7 ke Pas cyclic subgroup hoga Hume kese pata ki Jo order 10 Ka subgroup h vo cyclic ki hoga?
Because it must have elements of order 10
Thanku so much sir ❤❤
At 9:53 why Z2 is automorphic to K1 subgroup of S3?
ya I'm also confuse
I am one of your viewer , sir please kuch questions karaiye har topic par
sir can u plz tell ye topic kis book mein milega ... gallian and dummit foote mein to hai nhi .
plz sir reply ....🙏🏻🙏🏻🙏🏻
not in any book ,, we just apply theory
@@MathematicalScience ok sir g, thnks . u r providing very unique information thro ur videos thnx a lot🙏🏻🙏🏻🙏🏻
= how it possible please tell sir 1:45
8Modulo 8=0
@@MathematicalScience kk thanks sir
Sir H1={0} agar generator h z8 mein to ye bhi to group ke Sare elements generate Kar sakta h na jese 0+1,0+2.... Hum use sirf trivial subgroup kyo keh rhe h please clear this doubt
Trivial having only identity element
Bro you are explanation is to much good
Thank you bro
Sir in the 2nd example in case 3,, you said it will be isomorphic to Z4,, but it will be isomorphic to K4 as well??? So basically we have to find number of subgroup isomorphic to K4 in S8 as well???
Is there any general formula for finding number of group homomorphism from Zn to Sm ?
See the full playlist, you can generate formula yourself
plz also tell how to find automorphisms of dihedral subgroups or groups like D6
|Aut(Dn)|= n Phi(n)
Mathematical Science can u upload a video for that plz
@13.36 time, how z8/(0) is isomorphic to z8 ? why can't it be isomorphic to non abelian group D4 or Q8 which has 8 elements? Q8 is quarternian group, D4 is dihedral group
Just in one line by FTH
@@MathematicalScience Why can't it be isomorphic to Q8 or D4?
@@ravishkumar8422 a(0) tpye elements honge quotients group Mai where a belong to quoitient group.
Now ae is always a since e is identity.
@@humanity3049 I didn't get your explanation. Would you elaborate on it??
@@ravishkumar8422 z8/(e) ~z8 always
Because quotient group of z8/(e) contains all the right or left cosets of z8
a(e) type ke elements where (a) belong to z8.
Now take a=1, 2,3,4...
And form quotient group z8/(e)
Normal series,composition series, Solvable group, Nilpotent group, sylow theorem proof videos kindly upload sir
i will start Sylow soon
How many onto homomorphism from Q8 to Q8 ?
Aut(Q8)=24
@@MathematicalScience automorphism including both one one and onto
I just want to count onto
and there may be possibility s.t. some homomorphism are onto not one one so that such type of homomorphism are also included.
@@mohit9798 there is only 24 onto homomorphism, else are not onto
@@MathematicalScience ok sir thank you
Total no. of homomorphism from Q8 to Q8 ?
Sir S3 to S4 bta dijiye
plz try urself