Math 361, Spring 2013, Assignment 9

Carefully define the following terms, then give one example and one non-example of each:

1. Sylow \(p\)-subgroup.
2. Normalizer of a subgroup.

Carefully state the following theorems (you need not prove them):

1. Sylow's First Theorem.
2. Sylow's Second Theorem.
3. Sylow's Third Theorem.
4. Theorem on solvability of groups of prime power order (Theorem 37.1 in the text).

Do the following problems:

1. Section 36, problems 1, 2, 3, 4, 5, 13, 17, and 18.