Abstract Algebra: We consider the left regular action of G on the set X = G. We prove Cayley's Theorem, that every group is isomorphic to a subgroup of a symmetric group, and note a variant when X=G/H. As an application, we show that every group of order p^2 with p prime is abelian.
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.