Abstract Algebra

Orbit-Stabilizer Theorem

📋

Variables:

Description/Usage:

Relates the size of an orbit of an element to the size of its stabilizer and the whole group. It’s a foundational result in group actions, often used to count objects via Burnside’s lemma. Think of splitting the group's action into independent moves on \(x\) (orbit size) and those that do nothing to \(x\) (stabilizer).