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| Name | Cyclic Groups, Generators, and Cyclic Subgroups | Abstract Algebra |
| Video Uploader | Video From Wrath of Math |
| Upload Date | This Video Uploaded At 31-10-2022 00:00:14 |
| Video Discription | We introduce cyclic groups, generators of cyclic groups, and cyclic subgroups. We discuss an isomorphism from finite cyclic groups to the integers mod n, as well as an isomorphism from infinite cyclic groups to the integers. We establish a cyclic group of order n is isomorphic to Zn, and an infinite cyclic group is isomorphic to the integers. Finally, we introduce cyclic subgroups, and show the powers of an element will always form a cyclic subgroup. #abstractalgebra #grouptheory Every Cyclic Group is Abelian: https://youtu.be/MN32KnJSXR4 Every Subgroup of a Cyclic Group is Cyclic: https://youtu.be/D2DjlraX85o A Cyclic Group of Permutations: https://youtu.be/QQIYcoUZLPk Abstract Algebra Course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN Abstract Algebra Exercises: ◉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: https://www.patreon.com/join/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: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Math Rap channel: https://www.youtube.com/channel/UCQ2UBhg5nwWCL2aPC7_IpDQ/featured |
| Category | Education |
| Tags | wrath of math | math lessons | math | education | math video | abstract algebra | cyclic groups | cyclic subgroups | cyclic group generators | generators abstract algebra | cyclic groups proof |
