Read: Finish Section 2.3 and start Section 2.4.
Turn in: 2.42, 2.43, 2.44, 2.48, 2.49, 2.52, 2.55
Remarks
- On Problem 2.48, the goal is to simply rewrite Theorem 2.47 using “additive notation.” See Remark 2.46 in the book. The point is that for an abstract group, $gh$ and $g+h$ mean the same thing (as do $g^n$ and $ng$); we are just representing the binary operation multiplicatively in the first case and additively in the second. We will never mix multiplicative and additive notation in the same problem, but some problems will use one and some the other. When a group is abelian (i.e. the operation is commutative), we often use additive notation (but not always).
- Please make sure to read Theorem 2.47 (and try to prove it too)! Bring any questions you have, and I’ll make sure to talk through parts of it in class.
