What is the order of any element is a group of order three?
Can any non-identity in the group generate the group?
Are cyclic groups Abelian?
I have some modern algebra homework due tomorrow (and a midterm in there, ) and I've done all of the homework except this problem. I can't for the life of me figure out why a group of order 3 is abelian. I don't see the correlation between a groups order and whether or not a group is communitive.
Do any of you guys have any idea how to show this? Or could you just give me some hints that will get me started?
So, it's because every element in a group of order 3 has order 3, and the entire group can be generated by a non-identity element? Because it can be generated by a non-identity element, the group is cyclic, and every cyclic group is abelian?
Sorry if this seems like a really dumb question. I'm just really burning out on math. I have 2 math midterms tomorrow, and one next week, and I've been cramming hard core for a while now for it.