counting theorem


Given a group actionMathworldPlanetmath of a finite groupMathworldPlanetmath G on a finite setMathworldPlanetmath X, the following expression gives the number of distinct orbits

1|G|gGstabg(X)

Where stabg(X) is the number of elements fixed by the action of g.

Title counting theorem
Canonical name CountingTheorem
Date of creation 2013-03-22 12:22:23
Last modified on 2013-03-22 12:22:23
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 12
Author mathcam (2727)
Entry type Theorem
Classification msc 20M30
Synonym Cauchy-Frobenius-Burnside formula