Normal Subgroup
A subgroup is normal when for every and ; write .
Definition 7.1 (Normal Subgroup)
is called a normal subgroup if for all , we have . If so, we write .
Examples
The trivial subgroup and the whole group are normal in any group. Every subgroup of an abelian group is normal. In the dihedral group, , while is not normal. The kernel of a group homomorphism is normal.
Related
Stated in
- Definition 7.1 (Normal Subgroup)§7.1 Normal Subgroups