Stabilizer

Author

Eric W. Weisstein
December 6, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/Stabilizer.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Stabilizer.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Code

Stabilizer[pg_,a_]:=Select[gamma,#[[a]]==a&]

Example

gamma={{1,2,3,4},{2,1,3,4},{1,2,4,3},{2,1,4,3}};

PermutationGroupQ[gamma]

{#,Stabilizer[gamma,#]}&/@Range[4]//ColumnForm

Orbit

Orbit[pg_,a_]:=Union[Flatten[Position[#,a]&/@pg]]

Orbit[gamma,#]&/@Range[4]