Math 361, Spring 2015, Assignment 14

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

1. Normalizer (of a subgroup).

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

1. Theorem relating cardinalities of finite $G$-sets to cardinalities of their fixed point sets when $G$ has prime power order.
2. Cauchy's theorem.
3. Sylow's First Theorem.
4. Sylow's Second Theorem.
5. Sylow's Third Theorem.

Solve the following problems:

1. Section 36, problems 1, 2, 3, 4, 5, and 6.
2. Classify the groups of order 6 (i.e. give a list of groups of order six, such that every group of order 6 is isomorphic to exactly one group on your list).

--------------------End of assignment--------------------