Abstract Algebra

Problems taken from Chapter 4 - Cyclic Groups.

Problems

1. Problem 5 - Instead of \(\mathbb{Z}_{18}\), do this for \(\mathbb{Z}_{12}\).
2. Problem 9
3. Problem 14
4. Problem 23 - Skip part (a) since we did this in class.
5. Problem 24 - Hint: See Corollary 4.14. Your answer should be in terms of \(p\) and \(q\). Try this for small \(p\) and \(q\) to get an idea of the general method.
6. Problem 32 - This should not take you long; if it is then review the main theorems in this chapter.
7. Problem 39 - If \(d \mid m\) then \(m = d\cdot k\) for some integer \(k\in\mathbb{N}\). If \(g\) is a generator of \(G\) then consider \(g^k\).