Cycle (permutation)

A cycle is a type of permutation.

Let $S_M$ be the symmetric group on a set $M$ . Let $\zeta$ be an element of $S_M$ , and let $\bar{\zeta}$ be the subgroup of $S_M$ generated by $\zeta$ . Then $\zeta$ is a cycle if $M$ has exactly one orbit (under the operation of $\bar{\zeta}$ ) which does not consist of a single element. This orbit is called the support of $\zeta$ , and is sometimes denoted $\text{supp}(\zeta})$ (Error compiling LaTeX. Unknown error_msg).

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Cycle (permutation)

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