Abstract Algebra: Using conjugacy classes, we give a second proof that A5, the alternating group on 5 letters, is simple. We adapt the first proof that A5 is simple to show that An is simple when n is greater than 5. The key step is to show that any normal subgroup with more than the identity contains a 3-cycle.
U.Reddit course materials available at ureddit.com/class/23794/intro-to-group-theory Master list at mathdoctorbob.org/UReddit.html
Includes course on Group Theory (problems and solutions at website) and Ring Theory, and Field Theory. For Prerequisites on proofs and sets, see the Math Major Basics course.