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.
Introduced in 2010
(8.0)