conjugate stabilizer subgroups

Let be a right group action of G on a set M. Then


for any αM and gG. 11Gα is the stabilizerMathworldPlanetmath subgroupMathworldPlanetmathPlanetmath of αM.



and therefore Gαg=g-1Gαg.

Thus all stabilizer subgroups for elements of the orbit G(α) of α are conjugate to Gα.

Title conjugate stabilizer subgroups
Canonical name ConjugateStabilizerSubgroups
Date of creation 2013-03-22 13:21:44
Last modified on 2013-03-22 13:21:44
Owner Thomas Heye (1234)
Last modified by Thomas Heye (1234)
Numerical id 7
Author Thomas Heye (1234)
Entry type Derivation
Classification msc 20A05
Related topic Orbit