Group

A group is an algebraic structure. A group consists of an underlying set of objects, G<\math>, and a binary operation, *<\math>, and satisfies the following properties:


 * 1) Closure For all x,y \in G<\math> we have x*y\in G<\math>
 * 2) Associativity For all x,y,z \in  <\math> we have that x*(y*z)=(x*y)*z<\math>.
 * 3) Identity There exists an element e\in G<\math> such that for all  g\in G<\math> we have that e*x=x*e=x<\math>
 * 4) Inverse For all g\in G<\math> there is an element g^{-1}\in G<\math> such that g*g^{-1}=g^{-1}*g=e<\math>.

With this notation, a group may be specified as <\math>.