Master Cyclic Groups, Generators & Subgroups in Abstract Algebra ๐
Unlock the fundamentals of cyclic groups, generators, and subgroups with this comprehensive guide. Join Wrath of Math for full access to videos and notes to deepen your understanding!

Wrath of Math
52.3K views โข Oct 31, 2022

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Abstract Algebra course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN
Abstract Algebra exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz
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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
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https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
๐ 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
โ DONATEโ
โ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons
โ Donate on PayPal: https://www.paypal.me/wrathofmath
Follow Wrath of Math on...
โ Instagram: https://www.instagram.com/wrathofmathedu
โ Facebook: https://www.facebook.com/WrathofMath
โ Twitter: https://twitter.com/wrathofmathedu
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Views
52.3K
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831
Duration
10:38
Published
Oct 31, 2022
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