BUILT-IN MATHEMATICA SYMBOL

# GroupStabilizerChain

GroupStabilizerChain[group]
returns a list of successive stabilizers in group of the points in a base of group.

## Details and OptionsDetails and Options

• A base of a group is a list of points of its domain of action such that the only element in the group fixing them all is the identity.
• GroupStabilizerChain gives strong generators for a group, automatically choosing an appropriate base.
• An explicit base can be specified by setting the GroupActionBase option.
• For a base the stabilizer chain is given as a list of elements of the form {b1, ..., bi}->GroupStabilizer[group, {b1, ..., bi}] with . The first element is the stabilizer of , which is the complete group. The last element is the stabilizer of the base, which is the trivial group.
• The list of generators of each stabilizer is a subset of the list of generators of the previous stabilizer in the list. Therefore they are strong generators for the respective groups.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Stabilizer chain for a group:

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These are strong generators for the group:

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This is a base for the group:

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