BUILT-IN MATHEMATICA SYMBOL

GroupSetwiseStabilizer

GroupSetwiseStabilizer[group, {p₁, ..., p_n}]
returns the subgroup of group for which the images of the points are still in the list .

GroupSetwiseStabilizer[group, {p₁, ..., p_n}, f]
returns the setwise stabilizer subgroup under the action given by the function f.

Details Details

Group elements in the setwise stabilizer do not necessarily fix the points .
The pointwise stabilizer of a list of points, computed with GroupStabilizer, is a subgroup of the setwise stabilizer of the same list of points.
The output is a subgroup of group defined by generators, but possibly using different generators.
For permutation groups, the default group action is taken to be PermutationReplace.