Definition:Alternating Group

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

For any $\pi \in S_n$, let $\sgn \paren \pi$ be the sign of $\pi$.

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

Also known as
Some authors use $A \paren n$ for $A_n$.

Also see

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