Introduction to Group Theory

Introduction to Group Theory

A group is a nonempty set G with a binary operation * satisfying the following properties:

1. (Identity) There is a unique element e so that e*x = x and x*e = x for all x in G.
   
2. (Inverses) For every x in G there exists y in G so that x*y = e and y*x = e.
3. (Transitive) For every x, y, z in G we have (x*y)*z = x*(y*z).