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: • Isomorphic Groups and ...
Basic Properties of Homomorphisms: • Proof: Basic Propertie...
Examples of Group Homomorphisms: coming soon
Kernels of Homomorphisms: • Kernels of Homomorphis...
Abstract Algebra Course: • Abstract Algebra
Abstract Algebra Exercises: • Abstract Algebra Exerc...
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
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Негізгі бет Intro to Group Homomorphisms | Abstract Algebra
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