GroupStabilizer

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

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