# Definition:Alternating Group

## Definition

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

For any $\pi \in S_n$, let $\map \sgn \pi$ 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 $\map A n$ for $A_n$.

## Also see

• Results about alternating groups can be found here.