GroupSetwiseStabilizer

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

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

DetailsDetails

  • 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.
  • Evaluation of for an action function f, a point p and a permutation g of the given group, is assumed to return another point p'.
  • For permutation groups, the default group action is taken to be PermutationReplace.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Setwise stabilizer of four points:

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Take an element of the stabilizer:

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It moves the points of the list among them:

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Introduced in 2010
(8.0)
| Updated in 2012
(9.0)