I am trying to refresh my knowledge of modern algebra, and have come across a question in Gillian 8th ed. that I don't quite remember how to prove.
The question is:
For $n \geq 3$, describe the elements of $D_n$. How many elements does $D_n$ have?
I want to prove that $D_n$ is a complete set (I know it has $2n$ elements). I assume the general structure would be to prove that the list of symmetries (we'll call it $L$) is contained in the set of symmetries (we'll call it $\Sigma$), and then the other way, $\Sigma \subseteq L$.
If someone could point me in the right direction it would be much appreciated!