Cyclic Permutation/Examples/Non-Cyclic Element of S4

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Example of Non-Cyclic Permutation

Not all permutations are cycles.

Here is an example (written in two-row notation) of a permutation of the Symmetric Group on 4 Letters which is not a cycle:

$\begin{pmatrix} 1 & 2 & 3 & 4 \\ 2 & 1 & 4 & 3 \end{pmatrix}$


Sources