Definition:Symmetry Group of Line Segment

Group Example

Let $AB$ be a line segment.

The symmetry mappings of $AB$ are:

The identity mapping $e$

The rotation $r$ of $180 \degrees$ about the midpoint of $AB$.

This group is known as the symmetry group of the line segment.

Cayley Table

The Cayley table of the symmetry group of the line segment can be written:

$\begin{array}{c|cccccc}

 & e & r \\

\hline e & e & r \\ r & r & e \\ \end{array}$

Also see

• Symmetry Group of Line Segment is Group
• Symmetry Group of Line Segment is Symmetric Group

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Definition of Group Structure: $\S 26 \eta$