Definition:Parity Group

Definition
This has several forms, all of which are isomorphic:

etc.
 * The group $\struct {\Z_2, +_2}$
 * $C_2$, the cyclic group of order 2
 * The group $\struct {\set {1, -1}, \times}$
 * The quotient group $\dfrac {S_n} {A_n}$ of the symmetric group of order $n$ with the alternating group of order $n$

It is the only group with two elements.

Also see

 * Parity Group is Group
 * Parity Group is Only Group with 2 Elements