Question

what are the properties of normal subgroup​

Answer 1

Every subgroup N of an abelian group G is normal, because. A group that is not abelian but for which every subgroup is normal is called a Hamiltonian group. The center of a group is a normal subgroup. More generally, any characteristic subgroup is normal, since conjugation is always an automorphism.

Answer 2

Every subgroup N of an abelian group G is normal, because. A group that is not abelian but for which every subgroup is normal is called a Hamiltonian group. The center of a group is a normal subgroup. More generally, any characteristic subgroup is normal, since conjugation is always an automorphism