Group Actions

Paper , Order, or Assignment Requirements

Explore the notion of an action of a group on a set.Examples are the symmetric group Sn acting on the set of positive integers or the group of all invertible matrices in R^3×3 acting on the vector space R^3.The essay should discuss at least a general definition of a group action,the notion of orbit and examples.A further question that could be addressed is this:How can a group act on itself and what would be the orbits in such cases.