Introduction to Group Homomorphisms in Abstract Algebra

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We introduce group homomorphisms with the definition, the definition of a homomorphic image, and several examples, including proof that certain functions are homomorphisms. We also show a non-example, a function from one group to another which is not a homomorphism. In short, a homomorphism f from a group G to a group H, is a function from G to H such that for all a, b in G, f(ab) = f(a)f(b). We say the homomorphism "preserves the group operation". #abstractalgebra #grouptheory

Group Isomorphisms: https://youtu.be/fGqx_-F7zN4
Basic Properties of Homomorphisms: https://youtu.be/7tRDyAbgrJ8
Examples of Group Homomorphisms: coming soon
Kernels of Homomorphisms: https://youtu.be/j8SQDZ96LVs

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0:00 What is a Homomorphism?
0:40 Definition of a Homomorphism
2:59 Definition of Homomorphic Image
4:30 Example 1 (A homomorphism that is onto)
10:09 Example 2 (A homomorphism that is not onto)
11:42 Trivial Examples of Homomorphisms
12:25 Non-Example (A function that is not a homomorphism)
13:03 Two Basic Properties of Homomorphisms