Dihedral Group D4/Center

Center of the Dihedral Group $D_4$
Let $D_4$ denote the dihedral group $D_4$, whose group presentation is given as:

The center of $D_4$ is given by:
 * $\map Z {D_4} = \set {e, a^2}$

Proof
From Center of Dihedral Group:
 * $\map Z {D_n} = \begin{cases} e & : n \text { odd} \\ \set {e, \alpha^{n / 2} } & : n \text { even} \end{cases}$

Hence the result.