Proof that G is an Abelian Group if f(a) = a^(-1) is a Homomorphism

[@BrianCarloRivera]

I like these kinds of videos math sorcerer. please make a playlist regarding you proving stuff from advanced calculus. From Royden

[@demongeminix]

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.

[@bengtbengt3850]

Nice to see some proofs from group theory. I hope to see more soon!

[@eflat6522]

These problems you work out are still above my skill level, but I still watch them hoping to still learn something.:-)

[@TheMathSorcerer]

That's really good. Anything you learn is amazing:)

[@malawigw]

I have discovered a truly marvelous proof of this, which this comment box is too small to contain

[@TheMathSorcerer]

Lol!!!!

[@mimicoolll0]

i just gotta say you’re one of my favorite youtubers ever!

[@Raze968]

Nice keep up the good work!

[@Mathstoon]

nicely explained

[@TheMathSorcerer]

Thank you 😃

[@dreimikemount666]

Brought me back memories of a 1-semester study-unit "Groups & Vector Spaces" from the 1st year of my BSc Maths degree.

[@josesilesramirez4430]

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.

[@acdude5266]

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.

[@kundananji.simutenda]

Proff requesting if you can make more videos on mathematical statistics.

[@Kavyakavya-sr5rd]

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 💜🥺

[@God-ld6ll]

wondering why it isn't more often called a communitive group being autological. If i am correct on that.

[@tamptus3479]

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.

[@skypowell6955]

very good, proud of you. keep it up.

[@kilian8250]

You can also show the other direction, that if G is abelian then it is a homomorphism.

[@iamjoey6115]

Make more of these videos please

[@TheMathSorcerer]

Will do!

[@WitchidWitchid]

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.

[@MrMegatherium]

In this problem, can we assume f has an inverse? I used it in my proof, but I am not sure if it's right.

[@hubomba]

Riemann Hypothesis next.

[@MrMegatherium]

I can't assume it.