Permutation groups
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Symmetry groups are also permutation groups
Equations are omitted for technical reasons - download the original pdf
The group of symmetries of an equilateral triangle is an example of a permutation group. If we label the vertices of an equilateral triangle, we can see that each symmetry can be regarded as a rearrangement of these labels - that is, as a permutation. [Diagram goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it.] [Diagram goes here - download the original to see it.] [Diagram goes here - download the original to see it.] Reflection Q2 Reflection Q3 [Diagram goes here - download the original to see it.] [Diagram goes here - download the original to see it.] Rotation R1 [Diagram goes here - download the original to see it.] As the example illustrates a permutation of the symbols 1,2,3,… is a one-one mapping (a bijection) from the set {1,2,3,…} to itself.
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Contents of
Permutation groups
1 Permutation groups
2 Symmetry groups are also permutation groups
3 Symmetry group of the square
4 Rotation through phi
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