Question

Fun Exercise: Show that cyclic groups are abelian.

Answer 1

Let \(g\) be a generator \[g^ig^j = g^{i+j} = g^{j+i} = g^jg^i \]

Answer 2

Aced, xD.

Answer 3

I'm currently grading my students, and these are the types of questions that we asked them. :-P They're not doing so well, though...

Answer 4

I think abstract algebra might be hard w/o taking elementary number theory first

Answer 5

That makes sense, though elementary number theory felt way harder to me than abstract algebra did back in the day...

Answer 6

these cyclic groups and generators thingy becomes realy easy once you relate them to primitive roots and stuff

Answer 7

Interesting. I've seen primitive roots of unity only in two courses: complex analysis and graduate-level abstract algebra.

Answer 8

primitive roots show up in theory of indices and cryptography part of NT

Answer 9

I intuitively knew that rotations in the 2D plane were commutative, it's interesting to see that that this is supposedly how you prove this.

Answer 10

I am now annoyed because I have to trade a survey of algebra class for some required to graduate crap (that is, "science, technology, and society" aka "humanities" for engineers)

Answer 11

lol That sucks!