Proof of the Fundamental Homomorphism Theorem in Abstract Algebra

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We introduce and prove the fundamental homomorphism theorem (also called the first isomorphism theorem), which states that every homomorphic image of a group G is isomorphic to the quotient group of G by the kernel of f, given that f is a homomorphism from G onto H. To prove this we will use some prior results. We previously proved that a quotient group of G is a homomorphic image of G, so we now have that a group is a quotient group of G if and only if it is a homomorphic image of G (or isomorphic to one). So homomorphic images and quotient groups are somewhat interchangeable. #abstractalgebra #grouptheory

Proof f(a)=f(b) iff Ka=Kb: https://youtu.be/BlCU-Kr78qs
Normal Subgroups: https://youtu.be/kbT5SyF3H60
Coset Multiplication on Normal Subgroups: https://youtu.be/DJyOdMBUdnM
Kernels of Homomorphisms: https://youtu.be/j8SQDZ96LVs
Quotient Groups and Homomorphic Images: https://youtu.be/MKDAZV0XasI

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