# Alternating Group on 3 Letters

## Group Example

Let $S_3$ denote the symmetric group on $3$ letters.

The alternating group on $3$ letters $A_3$ is the kernel of the mapping $\sgn: S_3 \to C_2$.

$A_3$ consists of the $3$ elements:

$A_3 = \set {e, \tuple {123}, \tuple {132} }$

where the tuples denote cycle notation.

Thus $A_3$ is an instance of the cyclic group of order $3$.