##  [Orbit–Stabilizer Method](/index.php/orbit-stabilizer-method) 

  ##  [Orbit–Stabilizer Method](https://puremath.quantumdictionary.io/orbit-stabilizer-method-0) 

  

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Definition

A method using a group action on a set that applies the orbit–stabilizer relationship |Orbit(x)| = [G : Stab(x)] (or its group-theoretic analogues) to relate sizes or indices of orbits and stabilizer subgroups, enabling counting arguments and structural deductions about actions, conjugacy classes, and quotient sets.