Cyclic Groups 4

Let G be a group and let a ∈ G. Prove that if |a| = n and k ∈ ℤ, then a^k = e if and only if n divides k.

[@sapwho]

Super grateful for your work :-) I’m 16 and graduated HS this May and I am considering majoring in mathematics. I’ve been learning a lot of new topics including abstract algebra to see if I really want this, and your content makes this so much easier since sometimes books really don’t make sense. Question: Is this an *implication* of Lagrange’s theorem?

[@j-invariant]

Love the content, eerie ass music, you should change it or replace it with your own narration in the future

[@learnifyable]

I've been choosing random ambient music without thinking about it too much. I figure that people can mute it if they don't like it, but yeah, this one is particularly eerie. I'd like to start adding narration--just working on figuring out a good setup.