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

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

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First time I did understand! THANK YOU FOR YOUR EXPLANATION.

djb

I love to see the algebra content coming in!

kqnrqdtqqtttel

I believe that for showing the map is injective it suffices to note that since f is a group, all its elements have a unique inverse. Namely, if two inverses are equal to one another, the elements whos inverses are being taken must be equal, or that would contradict uniqueness. I feel like your method was more concrete though. Great vid as always!

thetheoreticalnerd

Nice Algebra proof. Although i'm only at the beginning of my math journey, i will someday get to abstract algebra. To me it seems like one of the more interesting fields of advanced math. Thank you for all your guidance!!! now the long path to abstract algebra is clear.

daniellindner

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

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

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