Cyclic Groups (Abstract Algebra)

Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra.
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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
www.jmilne.org/math/CourseNote...
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Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
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[@Socratica]

If you'd like to learn more, we have a free course on Group Theory! www.socratica.com/courses/group-theory

[@IamRigour]

Doesn't the set of all nth roots of Unity, a subset of complex numbers with modulus of 1, form a group whose operation is multiplication? Also, isn't this group cyclic? In Abstract Algebra (Theory and Applications) by Thomas W. Judson, it is mentioned that the set of all nth roots of Unity forms a cyclic group.

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You are so kind, thank you! Our dearest wish as well! :) We'll keep making videos and hopefully the viewers will come. Everyone share with your friends!

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Thank you Socratica! Your videos are wonderful and have given me new determination to continue my abstract algebra course. One of your greatest strengths (for me personally), is having well explained examples to accompany all your definitions and explanations. Most lecturers at the Tertiary level just tend to spout off theorems and definitions without actually showing any applicability to what we are learning- so this has completely changed the way I understand my maths. I will definitely be sharing this with all of my peers. Thank you again :)

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[@Socratica]

Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra

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Explanation and content is really perfect. One suggestion for abstract algebra videos if you can explain each concept of group with diagram... like small representative model then it will help us in complex concepts. thanks a lot for videos. Appreciated all your work.

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Las explicaciones son bastante claras, me gustaría que subiera un vídeo en castellano. Gracias por el gran aporte en el aprendizaje del álgebra abstracta.

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I think that the point of this series is to introduce modern algebra. If you just watched this series to pass abstract algebra, you would most definitely fail.

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These videos are helping me pass Abstract Algebra I swear.

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[@sofiasarigiannidi8708]

This is very well done but I wish there was more talk upon the definition of a generator and also that the cyclic groups are the only ones up to isomorphisms

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[@2bsirius]

For more detail on this check out a video playlist from Harvard: Abstract Algebra/Group Theory. It has a great set of lectures by Harvard math prof, Benedict Gross which incorporate cyclic groups as well as many other concepts in abstract algebra.

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[@jaimeduncan6167]

Hi, excellent work and explanation. You say that all the cyclic groups are the integers or the integers mod n. I guess you were trying to avoid the use of isomorphic (correct me if I am wrong ) to avoid confusion. Maybe using “behaves as , or is identical to “ instead , but my idea could end up confusing people even more 😊 but there I let my 3cents. Critical students will be able to create groups that are not the integers and are cyclical.

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