Midterm One Typos

Dear Class,

Here I'll keep a running list of typos. I hope they aren't too long.

Also, I will update the midterm PDF file with blue font as typos are corrected.

1. In Problem 1(c), we should have that   "f \star e = e \star f = f".
2. Clarification: In problem 3, the + in the expression "phi_1(a) + phi_2(a)" is the group operation in B. On the other hand, the + in "phi_1 + phi_2" also stands for an operation on the set of homomorphisms from A to B; in fact, one can show that this makes hom(A,B) into an abelian group, too; but that's not required in the problem.
3. In problem 2(b), you need to assume that the kernel of pi' contains A. I've updated the pdf file (and the wording in 2(a)) to indicate this.
4. In Problem 3(e), you should prove your answer for all choices of theta.
5. In problem 4, the matrix rho(g) should ahve (i,j)th entry equal to 1 if and only if g(j)=i.
6. Also in problem 4(c), you should prove that your interpretation is correct in all possible cases.