Math 254A. Homework 8

Due Wednesday, 18 October

1. Let K = ℚ(\sqrt{223}). (a). Find a fundamental unit for K. (b). Compute the class group of K, and give explicit generators and relations.

[Hint: Use your answer to (a).]

Do not rely on the tables handed out in class, and do not rely on computers to find these answers for you.

2(nc). Exercise 7 on page 52. Assume that p is an odd prime. (For a permutation π, sgn π is 1 if the permutation is even and −1 if it is odd.)

3(nc). Exercise 9 on page 52.