This video should be after the isomorphism theorems. At this point, I don't know what is kernel, group division (are there quotient group videos?), or what happened to the injectivity requirement in the second example. EDIT This video is premature, and the next videos clarify it all (including referencing this video in its right order).
Great video. How can the infinite group of the integers be isomorphic to the finite group formed by the integers modulo n? They do not have the same cardinality trivially.
at 41:30... If A is the matrix [(a,0)(0,a)], would then not phi([(a,0)(0,a)]) not map to 1/(a*a) *A = 1/(a*a) * [(a,0),(0,a)] = [(1/a,0),(0,1/a)] which is not necessary equal to the identity matrix?
I liked the D6 to S6 part around 34:10. I have a question for the hypothetical case from D6 to s4 and how i would reason to choose the Image to be {e, (12), (34), (12)(34)} and not for example (14) and (23) or would that work, too?
Very helpful! My abstract algebra class gets a little too abstract sometimes, its nice to have so many concrete examples.
One of the great bonusses of this course. The examples presented here are great. Very illustrative.
I wasn't planing to watch the entire video, as i don't like algebra very much, but with you talking the video was over, before i even realized.☺
At 21:00, I think the equation should be like phi(sr^n-1)=phi(s)+(n-1)phi(r)=1+0=1.
This video should be after the isomorphism theorems. At this point, I don't know what is kernel, group division (are there quotient group videos?), or what happened to the injectivity requirement in the second example.
EDIT
This video is premature, and the next videos clarify it all (including referencing this video in its right order).
ya, it confused me so much too ! ! !
thanks for your comment, now i know
Great video. How can the infinite group of the integers be isomorphic to the finite group formed by the integers modulo n? They do not have the same cardinality trivially.
This video deserves more views
Where is the prerequisite video about the order. You said we should watch it first.
PURE GOLD
REALLY helps, thank you!
Thanks a lot. Very clear and very useful!
at 41:30... If A is the matrix [(a,0)(0,a)], would then not phi([(a,0)(0,a)]) not map to 1/(a*a) *A = 1/(a*a) * [(a,0),(0,a)] = [(1/a,0),(0,1/a)] which is not necessary equal to the identity matrix?
You are right! Let me think if I can fix this example, otherwise I may cut it out.
For anyone reading this in the future: I cut this example out of the video.
I liked the D6 to S6 part around 34:10. I have a question for the hypothetical case from D6 to s4 and how i would reason to choose the Image to be {e, (12), (34), (12)(34)} and not for example (14) and (23) or would that work, too?
Hi sir Michael ..can you tell me where is the proof that the order of phi divides order of x ..I mean where can I find the video??
In the GL_2(R) ---> R^* you did not show that the map is surjective.
Great video thanks
Excelente
Thank you soooooo much!!!!!
Thanks a lot !