BUILT-IN MATHEMATICA SYMBOL

GroupSetwiseStabilizer

returns the subgroup of group for which the images of the points

are still in the list

.

MORE INFORMATION

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.

EXAMPLES

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Basic Examples (1)

Setwise stabilizer of four points:

Take an element of the stabilizer:

It moves the points of the list among them:

Setwise stabilizer of four points:

In[1]:=

Out[1]=

Take an element of the stabilizer:

In[2]:=

Out[2]=

It moves the points of the list among them:

In[3]:=

Out[3]=

Scope (2)

Compute the setwise stabilizer of a permutation group defined by generators:

Possible results of the action of the elements of the setwise stabilizer:

Compute the setwise stabilizer of a named permutation group:

Possible results of the action of the elements of the setwise stabilizer:

Properties & Relations (1)

Take the group:

And the list of points to stabilize:

Compute the setwise stabilizer:

And the pointwise stabilizer:

Check that the pointwise stabilizer is a subgroup of the setwise stabilizer:

Compare the possible reorderings of the list in both cases. The six reorderings correspond to the six cosets of the stabilizer in the setwise stabilizer: