Definition:Alternating Group

Definition
Let $S_n$ denote the symmetric group on $n$ letters.

For any $\pi \in S_n$, let $\operatorname{sgn} \left({\pi}\right)$ be the sign of $\pi$.

The kernel of the mapping $\operatorname{sgn}: S_n \to C_2$ is called the alternating group on $n$ letters and denoted $A_n$.

Also known as
Some authors use $A \left({n}\right)$ for $A_n$.

Also see

 * Alternating Group is Normal Subgroup of Symmetric Group
 * Alternating Group is Set of Even Permutations