301.6 Isomorphisms Problem Session (Live Stream)

The "Highlander Theorem:" There can be only one cyclic group up to isomorphism. And, given a prime p, there is only one group of order p up to isomorphism.
Isomorphisms preserve the order of elements. We prove it and use it to surface differences between groups.

[charlesterrel]

Really great work! Your passion for maths exudes throughout every element of your being!!! Thank you so much for sharing this video🙏🏾 your class is lucky to have

[heisenbergmuzik]

Fantastic lecture 👍.
I have one peculiar doubt which troubling me a lot.. plz help.
Whenever we are asked to prove non isomorphism we have quite a lot tools like order of group, order to order(elements), subgroups to subgroups, generator to generator etc. But while attempting to prove isomorphism (if given problem is isomorphic) I'm unable to find much at my disposal. Is there more of such tools like Highlander theorem which guarantee isomorphism? If so, please enumerate them. It would make my day.
Thank you.

[GopinathShanmugam]

Sir, how many homomorphisms are there A5 to S4?