Math 360, Fall 2013, Assignment 10

Mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning.

- John Locke, Second Reply to the Bishop of Worcester

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

1. Simple group.

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

1. Falsity of the converse of Lagrange's Theorem.

Solve the following problems:

1. Section 15, problems 3, 7, and 11.

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

Questions:

1. Somehow I got question 3 right. I thought I understood. But when I tried doing question 7 and 11, the oops came. So yeah, how do you do those questions anyways? I don't really get it.

Solutions:

1. Simple Groups: A group is simple if it is non trivial and has no proper nontrivial normal subgroups.

Example: The alternating group An is simple for N >= 5.