Cycle Decomposition/Examples/Permutation in S7

Example of Cycle Decomposition

Consider the permutation given in two-row notation as:

$\rho = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 5 & 6 & 1 & 7 & 3 & 2 & 4 \end{pmatrix}$

The cycle decomposition for $\rho$ is:

$\begin{pmatrix} 1 & 5 & 3 \end{pmatrix} \begin{pmatrix} 2 & 6 \end{pmatrix} \begin{pmatrix} 4 & 7 \end{pmatrix}$

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Symmetric Groups: $\S 80$