Скачать с ютуб Intro to Group Homomorphisms | Abstract Algebra в хорошем качестве

Intro to Group Homomorphisms | Abstract Algebra

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 Isomorphisms in...   Basic Properties of Homomorphisms:    • Proof: Basic Properties of Homomorphi...   Examples of Group Homomorphisms: coming soon Kernels of Homomorphisms:    • Kernels of Homomorphisms | Abstract A...   Abstract Algebra Course:    • Abstract Algebra   Abstract Algebra Exercises:    • Abstract Algebra Exercises   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 ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Abstract Algebra: https://amzn.to/3IjoZaO Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020