(Abstract Algebra 1) Cyclic Subgroups

A definition of cyclic subgroups is provided along with a proof that they are, in fact, subgroups.

[hamadalhajri]

I think you are a devoted, smart and a generous human being for spending this time and effort to explain this heavy subject. There is no doubt about you intelligence sir, But you are a great communicator too and know how deliver math arguments very well. Great job

[havock]

thank you so much for making these Abstract Algebra videos! This has helped me tremendously to get thru with my AA class in college!!

[GETURHANDSUP]

It is 3:00 a.m, and I understand this shit lol

[ftnsy]

this is immensely helpful i dont always thank people on youtube for their content but i feel the need to drop my appreciation on here anyhow since ur videos on abstract/modern algebra are my lifesaver!!

[Love_Hope_from_Above]

Professor Learnifyable:

Thank you for having produced an excellent video on cyclic groups.  I really like your step-by-step approach.  As cyclic group can be a very challenging topic (depending on the examples presented), would it be possible on your next video you do a few more challenging demonstrations such as the centralizer of a group and others found in the abstract algebra books by Fraleigh or Gallian?   When I first learned cyclic groups about one year ago, I had some trouble with it and it took me a few weeks to understand it.   Many thanks again for being a wonderful teacher!

    > Benny of California, 8-29-2014

[makuwaniblessing]

the first example the smallest subgroup that contains the element 2 ...we 2 subgroups including the 4Z

[NeelSandellISAWESOME]

At 4:05, don't you also have to show that the associative property holds and that the identity element exists in the group?

[koizumichiaki]

how to know the smallest subgroup element is 2 in z6? i am still learning for cyclic group and need more understanding.tq

[tinasofronieska]

Shouldn't we first prove that the subgroup generated by the element a is non-empty and then use the subgroup test? I know that the identity will be an element of that subgroup, hence the subgroup will be non-empty, but i think it should be written down.

[theodor]

Would love to see some example problems to cement the topic in hand. Some topics seem so abstract and it's hard to imagine what you would do on an exam but with an example problem it takes the edge off.

[gvzlqdh]

Hi but a little confused.. whats the difference of subgroup and generators?

[virtuousjoffrey]

How do we know that the binary operator here is multiplication?

[judym]

It's really helpfull, thank you 😄😄😄

[devangparekh]

@learnifyable is the order of the the abstract algebra playlist meant to be in this order? should i be watching this video before watching video 40 or 42?