# Orbit-stabilizer theorem

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Orbit-stabilizer theorem](https://ocme.evemisslab.com/en/atlas/atlas-orbit-stabilizer-theorem/)

For a complete finite group action, the orbit size and stabilizer size of the same point multiply to the group order.

atlas-orbit-stabilizer-theorem · canonical_mko

[Orbit-stabilizer theorem](https://ocme.evemisslab.com/en/mko/mko-orbit-stabilizer-theorem/)

## Prerequisite nodes


- [Orbit of a finite group action](https://ocme.evemisslab.com/en/atlas/atlas-finite-group-orbit/)
- [Stabilizer of a finite group action](https://ocme.evemisslab.com/en/atlas/atlas-finite-group-stabilizer/)
- [Cardinality comparison of sets](https://ocme.evemisslab.com/en/atlas/atlas-cardinality-comparison/)