Editing Group action (section)

=== Burnside's lemma ===
A result closely related to the orbit-stabilizer theorem is [[Burnside's lemma]]:
<math display=block>|X/G|=\frac{1}{|G|}\sum_{g\in G} |X^g|,</math>
where {{math|''X''<sup>''g''</sup>}} is the set of points fixed by {{math|''g''}}. This result is mainly of use when {{math|''G''}} and {{math|''X''}} are finite, when it can be interpreted as follows: the number of orbits is equal to the average number of points fixed per group element.

Fixing a group {{math|''G''}}, the set of formal differences of finite {{math|''G''}}-sets forms a ring called the [[Burnside ring]] of {{math|''G''}}, where addition corresponds to [[disjoint union]], and multiplication to [[Cartesian product]].