A group, G, is a set with a multiplication rule defined on it which must 
satsfy:
	1. gi*gj in G forall gi*gj (closure)
	2. gi*(gj*gk)=(gi*gj)*gk (associativity)
	3. There exists identity, e, s.t. e*g=g=g*e
	4. forall g in G there exists g-1 (g inverse) s.t. g*g-1=g-1*g=e

Groups express symmetries.  There are many examples of symmetries in nature
and this is why groups are useful in physics.

Some theorems:
 * H,K subgroups of G => H intersect K subgroup of G
 * H,N subgroups of G with N normal => H intersect N subgroup of H is normal w.r.t H
 * H,N normal subgroups of G => H intersect N subgroup of H is normal w.r.t G