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
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $9$: Permutations: Example $9.3$