\begin{definition}[Definition:Parity Group]
This has several forms, all of which are isomorphic:
:The group $\struct {\Z_2, +_2}$
:$C_2$, the cyclic group of order 2
:The complex square roots of unity $\struct {\set {1, -1}, \times}$
:The quotient group $\dfrac {S_n} {A_n}$ of the symmetric group of order $n$ with the alternating group of order $n$
and so on.
\end{definition}