Group Action/Examples/Cyclic Group on Polygon/Mistake

Source Work

 * action 3.
 * action 3.

Mistake

 * For example, the $n$-element ${}^*$cyclic group whose elements are $e, a, a^2, \ldots, a^{n - 1}$ acts on the vertices of a ${}^*$regular polygon by the map for which $e x$ is $x$ for each vertex $x$, and $a^k x$ is the vertex obtained when $x$ is rotated through $2 \pi k / n$ radians about the center of the polygon.

Correction
It is not $x$ which is rotated, it is the whole polygon.

Hence this would be better worded as:


 * For example, the $n$-element ${}^*$cyclic group whose elements are $e, a, a^2, \ldots, a^{n - 1}$ acts on the vertices of a ${}^*$regular polygon by the map for which $e x$ is $x$ for each vertex $x$, and $a^k x$ is the vertex obtained when the polygon is rotated through $2 \pi k / n$ radians about the center of the polygon.