returns the subgroup of elements of group that move none of the points p1, …, pn.
returns the stabilizer subgroup under the action given by the function f.
- 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.
Examplesopen allclose all
Basic Examples (1)
Subgroup of permutations that leave invariant a list of objects under Permute action:
Check that the corresponding orbit under Permute action contains only that list:
Properties & Relations (3)
A stabilizer subgroup computed with GroupStabilizer might be described using more generators than the original group:
Wolfram Research (2010), GroupStabilizer, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupStabilizer.html (updated 2012).
Wolfram Language. 2010. "GroupStabilizer." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/GroupStabilizer.html.
Wolfram Language. (2010). GroupStabilizer. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GroupStabilizer.html