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

Details 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 {b1,,bn} the stabilizer chain is given as a list of elements of the form {b1,,bi}->GroupStabilizer[group,{b1,,bi}] with i=0,,n. 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.


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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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Scope  (1)

Options  (1)

Applications  (1)

Possible Issues  (1)

Introduced in 2010