Let o: G1G2 be a surjection homomorphism between two groups, N be a normal subgroup of gi, and KerocN. Proof: G2/(N)is a group. Theorem 6.22: Let [H; be a normal subgroup of the group G; * Then G/H; o is a group. VP(N is a subgroup of g2. ◆ Normal subgroup? ◆g2op(n)g2∈?(N) ◆ For vg2∈G2,p(n)∈q(N),g1∈G1S.t q(g1)=g2 o surjection homomorphism Let : G1→G2 be a surjection homomorphism between two groups, N be a normal subgroup of G1 , and KerN. Proof: G2 /(N) is a group.  Theorem 6.22: Let [H;] be a normal subgroup of the group [G;]. Then [G/H;] is a group.  (N) is a subgroup of G2 .  Normal subgroup?  g2 -1(n)g2?(N)  For g2G2 , (n)(N), g1G1 s.t (g1 )=g2 ?  surjection homomorphism