A Group Theory Problem

I remember as a freshman in college I was given a group theory problem in an exam that I couldn't solve at the time. (There was no hints though ) I may have heard the solution later but a few days ago I was thinking about that problem. So here is the problem and some hints. It is a nice and challenging problem. You might want to think about it before looking at the solution. The solution will be posted later. Problem. Let be a group of size where is a prime number. Show that has a normal subgroup of size either or . Hint #1: Use the Sylow theorem and count the number of(more...)