---
tag: P2PYGK858D
kind: concept
name: Cycles and fixed points
sources:
  - wikipedia: en:2221032@r1153320071
    locator: Cycles and fixed points
    note: adopted
    mention: wikipedia://en/2221032
    sections: [Summary]
same_as:
  wikidata: Q5198198
  wikipedia: Cycles and fixed points
inventory: [WY6TJ1N446]
---

## Summary

In mathematics, the **cycles** of a [[permutation|05RWFKVTJ7]] $\pi$ of a finite [[set|0BSJ7RQ9BW]] **S** correspond [[bijectively|0151VYVX27]] to the orbits of the subgroup generated by $\pi$ acting on *S*. These orbits are [[subsets|0BJR9QR08E]] of **S** that can be written as $\{c_{1}, ..., c_{n}\}$, such that