This is pretty good, although I am always a bit worried that it is difficult for people to internalize this stuff without a real drive to get into abstract alge

This is pretty good, although I am always a bit worried that it is difficult for people to internalize this stuff without a real drive to get into abstract algebra. As a side note, I think a really nice way to go (dovetailing off of the ending group actions section) is to use group actions and this lemma (https://qchu.wordpress.com/2013/07/09/the-p-group-fixed-point-theorem/ https://qchu.wordpress.com/2013/07/09/the-p-group-fixed-poin...) to prove a bunch of cool stuff. It really unifies all of the basic stuff and makes it clear that finite group theory is really entirely about symmetries/actions.