At the beginning of this video Michael restated the Second Isomorphism Theorem. There is a mistake he made. Item one of this theorem is not N is normal in H intersect N. It should say N is normal in HN.
This proof is still just the coolest thing to me. It illustrates the concept of abstract groups in a much more tangible way with elementary number theory
Awesome proof- obviously more work than other ways- but really hits home the usefulness in studying group theory and the abstractness that comes with it….
At the beginning of this video Michael restated the Second Isomorphism Theorem. There is a mistake he made. Item one of this theorem is not N is normal in H intersect N. It should say N is normal in HN.
What you meant on the first two was:
1) N ⊲ HN
2) H∩N ⊲ H
so the validity of HN/N and H/(H∩N) as groups hold
After only recently studying the elementary proof of the lcm/gcd relationship as well as the isomorphism theorems, this proof was something special.
This proof is still just the coolest thing to me. It illustrates the concept of abstract groups in a much more tangible way with elementary number theory
Awesome proof- obviously more work than other ways- but really hits home the usefulness in studying group theory and the abstractness that comes with it….
Amazing