Section 10.1 Factor Groups and Normal Subgroups
Subsection Normal Subgroups
A subgroupExample 10.1.
Let
Example 10.2.
Let
Theorem 10.3.
Let
The subgroup
is normal inFor all
For all
Proof.
(1)
(2)
(3)
Subsection Factor Groups
IfTheorem 10.4.
Let
Proof.
The group operation on
Then
The remainder of the theorem is easy:
Example 10.5.
Consider the normal subgroup of
This group is isomorphic to
Example 10.6.
Consider the normal subgroup
The group
In general, the subgroup
The sum of the cosets
Example 10.7.
Consider the dihedral group
The element