Math 817: Problem set 3

Instructions: Write up any four of the following problems (but you should try all of them, and in the end you should be sure you know how to do all of them). Your write ups are due Friday, September 17, 2004. Each problem is worth 10 points, 9 points for correctness and 1 point for communication. (Your goal is not only to give correct answers but to communicate your ideas well. Make sure you use good English, so proofread your solutions. Once you finish a solution, you should restructure awkward sentences, and strike out anything that is not needed in your approach to the problem.)
  1. Let H and K be subgroups of a group G. If H and K are normal, show that both HK and the intersection I of H with K are subgroups which are normal in G.
  2. Let G be a group.
  3. This is #10, p. 74.