Dihedral Group D4/Subgroups/Cosets/Subgroup Generated by b

Examples of Cosets of Subgroups of Dihedral Group $D_4$
Let the dihedral group $D_4$ be represented by its group presentation:

Let $H \subseteq D_4$ be defined as:
 * $H = \gen b$

where $\gen b$ denotes the subgroup generated by $b$.

From Subgroups of Dihedral Group D4 we have:


 * $\gen b = \set {e, b}$

Right Cosets
It is seen that the left cosets do not equal the corresponding right cosets.

It follows by definition that $\gen b$ is not a normal subgroup of $D_4$.