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.

Be sure to subscribe so you don't miss new lessons from Socratica:

♦♦♦♦♦♦♦♦♦♦

We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition

Milne, Algebra Course Notes (available free online)

♦♦♦♦♦♦♦♦♦♦

Ways to support our channel:

► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9

Thank you!

♦♦♦♦♦♦♦♦♦♦

Connect with us!

♦♦♦♦♦♦♦♦♦♦

Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

♦♦♦♦♦♦♦♦♦♦

[erodotosdemetriou]

So thankful! In 5 min, you explained a one-hour no-sense university presentation! Not everyone with a PhD should become a professor. Some people are charismatic in explaining things while others are not so much!

[vanguard]

I wish a million subscribers on this channel

[e.jhumphrey]

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 :)

[DavidKotschessa]

This is very well done. I would not be terribly upset if you decide to do a series on algebraic topology.

[KenPryde]

I can't adequately express how fantastic this video series is, both in quality of the material, and the clear, informative, and accessible presentation.

[Babubro]

Fairly speaking
I accidentally watched your one video,
Now here iam watching each and every video with out a single skeep❤❤❤❤❤
Great mam,
Lots of love from Nepal

[ideedrafiqi]

Thanks Socratica!, I aced my Group Theory majors.

[SuperOpposum]

This is such an amazing playlist, making it all so simple and clear while doing it so much faster than my professor.
I immediately checked what other subjects you have, and it seems like I'll be using you guys next semester as well, so pleased.

[havock]

I love this series! It helped me a lot preparing for my Abstract Algebra exam!! Please try to make series for Real Analysis and Differential Geometry if you can! Not many well produced stuff for upper division math courses on Youtube.

[kellybrower]

The diagram for Integers mod n under addition has shown me the light. Thank you gorgeous stranger with the voice of power and mind of algebra.

[traciyandell]

A super channel. I'm using the Abstract Algebra section to get me through a class. The instructor is great! She adds humor and understanding of the concepts -- presents very well. Thanks for this channel!

[paulfrazier]

I have yet to take an actual class on abstract algebra (been studying it on my own because I find it fun), but these videos really fill in the holes of my understanding. I knew a fascination with axiomatic set theory would be useful someday!

[omkark]

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.

[salounik.]

Everything was good. I have my exams tomorrow and I found this good piece. I'm so happy.
And oh, that music at the end...lovely!

[alongimchen]

I accidentally clicked in this video and the way you teach is absolutely amazing...I've already subscribed your channel..I would kindly request you to upload more examples and videos on group theory .. thank you Ma'am

[moularaoul]

It hurts me to see these wonderful videos not reaching millions of views !!! Please can you also do some lessons on topology, complex analysis and differential geometry? Please!!!!

[deckfart]

Your videos have been really helpful, especially nowadays when we can't go to our Universities anymore. Thanks a lot.

[huutaiphung]

It's just so great, hope you will make more videos in Abstract Algebra

[aswathik]

your presentation is wonderful and to the point!!

[rasraster]

Isn't it more correct to say that all cyclic groups are isomorphic to Z and Z/nZ, rather than saying that those are the only cyclic groups?