Master Cyclic Groups, Generators & Subgroups in Abstract Algebra 📚

Support the production of this course by joining Wrath of Math to access all my Abstract Algebra videos plus lecture notes at the premium tier!
https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
🛍 Check out my math fashion brand! https://mathshion.com/

Abstract Algebra course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN
Abstract Algebra exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz

Get the textbook! https://amzn.to/45IvVgH
Business Inquiries: wrathofmathlessons@gmail.com

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

★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

Follow Wrath of Math on...
● Instagram: https://www.instagram.com/wrathofmathedu
● Facebook: https://www.facebook.com/WrathofMath
● Twitter: https://twitter.com/wrathofmathedu