I want to show that the dihedral group $D_n$ is nilpotent if and only if $n=2^i$ for some $i$.
I have shown the direction $\Leftarrow$.
Could you give me some hints for the direction $\Rightarrow$ ?
We suppose that $D_n$ is nilpotent and $n=2^im$, where $2\not\mid m$, or not?
How can we find a contradiction?