Math 361, Spring 2016, Assignment 14

Probably I am very naive, but I also think I prefer to remain so, at least for the time being and perhaps for the rest of my life.

-E. Dijkstra

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

1. Composition series (i.e. saturated subnormal series).
2. Composition factors.
3. Simple group.
4. Automorphism.
5. Inner automorphism.
6. Conjugate (subgroups).

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

1. Jordan-Hölder theorem.
2. Sylow's First Theorem.
3. Sylow's Second Theorem.
4. Sylow's Third Theorem.

Solve the following problems:

1. Section 35, problem 7.
2. Section 36, problems 1, 2, 3, 4, and 5.
3. Section 37, problems 5 and 6.

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