GroupStabilizer

GroupStabilizer[group,{p1,,pn}]
returns the subgroup of elements of group that move none of the points p1, , pn.

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

DetailsDetails

  • The output is a subgroup of group defined by generators, but possibly using different generators.
  • The stabilizer group is also known as the little group or isotropy group.
  • The stabilizer of a list of points is a subgroup of the setwise stabilizer of the same list of points.
  • Evaluation of f[p,g] 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)

A stabilizer subgroup of an alternating group:

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None of the permutations move any of the points {1,5}:

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