Definition:Symmetry Group of Line Segment
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Group Example
Let $AB$ be a line segment.
The symmetries 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
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Definition of Group Structure: $\S 26 \eta$