H is a subgroup of G iff H is a sunset of G and H satisfies all the axioms of
a group using the multiplication rule of G.
Theorems about subgroups:
1. If H and K are subgroups of G then H intersect K is a subgroup of G.
2. If H is a subgroup of G and N is a normal subgroup of G, then H
2. intersect N is a normal subgroup of H.
3. If H is a subgroup of G and N is a normal subgroup of G, then NH=HN
3. is a subgroup of G, not necesserily normal.
4. If H and N are both normal subgroups of G, then H intersect N, and
4. HN are both normal subgroups of G.