Sections 7.1-7.2 Due May 26

1. Does part 2 of theorem 7.5 imply that G is commutative, and hence an abelian group? When it started talking about order of an element, I didn't understand what e was. When it says "if a has a finite order n" is n the number of times you have to multiply a to get e? and therefore is n not unique?
2. Groups seem to follow traditional rules with exponentials, and overall still seem fairly simple. It's interesting that we didn't talk about order in rings, but only in groups. The corollary on the top of page 178 was interesting because I wouldn't have thought that such a correlation between the orders of elements would exist.