Wolfram Language & System 10.4 (2016)|Legacy Documentation

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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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Introduced in 2010