Proof that G is an Abelian Group if f(a) = a^(-1) is a Homomorphism
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- čas přidán 29. 06. 2022
- In this video I prove that G is an abelian group if f(a) = a^(-1) is a group homomorphism. This problem is from a book called "Foundations of Higher Mathematics" and it was written by Fletcher and Patty. This is a good book for learning to write proofs.
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Thank you:)
I like these kinds of videos math sorcerer. please make a playlist regarding you proving stuff from advanced calculus. From Royden
nicely explained
Thank you 😃
I used this book back in college in 2004 for a Math History class. I still have it.
If you're going to get it, get it used. The price for it new is outrageous.
These problems you work out are still above my skill level, but I still watch them hoping to still learn something.:-)
That's really good. Anything you learn is amazing:)
Nice to see some proofs from group theory. I hope to see more soon!
Thanks so much for this video. I will say that it is much better when you show your organic thinking and scratch work instead of presenting a clean well organized proof. It is better because we learn not just the results but also thinking strategies.
Nice keep up the good work!
I love maths and I'm mathematics ug student ... I fear about Abstract algebra but I love Maths... After ur video I will definitely fall in fearles love with abstract algebra.. thank you sir💜✨.. Keep doing these kind of playlist Sir 💜🥺
Nice problem to demonstrate basic group ideas, introducing homomorphisms in a proof using inverses of elements.
Gallian, Durbin, and Hernstein (out of print) are good intro books.
Proff requesting if you can make more videos on mathematical statistics.
i just gotta say you’re one of my favorite youtubers ever!
I have discovered a truly marvelous proof of this, which this comment box is too small to contain
Lol!!!!
Make more of these videos please
Will do!
Brought me back memories of a 1-semester study-unit "Groups & Vector Spaces" from the 1st year of my BSc Maths degree.
very good, proud of you. keep it up.
wondering why it isn't more often called a communitive group being autological. If i am correct on that.
Brings me back to my Group Theory days. I enjoyed figuring out those.types.of.proofs. I always liked to think about alternate ways to prove a theorem I. Except when I got stumped. Then I was just happy to discover any proof that would work correctly and at that point I would leave well enough alone...LOL.
We can see more: If G is not abelian and f:G->H and multiplication in H is swapped ( x (*H) y :-= y (*G) x ). Then f(a) = a^(-1)
is an isomorphism.
Is swapping allways isomorphic? No! There is a Loop (Quasigroup with neutral) with 5 Elements and swapping is not isomorh.
You can also show the other direction, that if G is abelian then it is a homomorphism.
Riemann Hypothesis next.