Definition:Alternating Group

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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.