O 6.4.4 Normal subgroups Definition 18: A subgroup H of a group is a normal subgroup if gh=g for VgEG. 4 Example: Any subgroups of Abelian group are normal subgroups ◆S3={e o5: 90192,03,04905 ◆H1={e,o};H2={e,a2};H3={e,3};H4={e, 4, 05 are subgroups of s3. Hg is a normal subgroup6.4.4 Normal subgroups  Definition 18：A subgroup H of a group is a normal subgroup if gH=Hg for gG.  Example: Any subgroups of Abelian group are normal subgroups  S3={e,1 , 2 , 3 , 4 , 5 } :  H1={e, 1 }; H2={e, 2 }; H3={e, 3 }; H4={e, 4 , 5 } are subgroups of S3 .  H4 is a normal subgroup