is an option to specify a base for a group.


  • 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.
  • Reordering the points in a base gives a different base.
  • The choice of base affects the ordering of group elements in the functions GroupElements and GroupElementPosition.
  • If the list of points given is not a base, the Wolfram Language will add more points until obtaining a base. In particular, GroupActionBase->{} will make the Wolfram Language choose an appropriate base.


Basic Examples  (1)

Elements of a group in standard order:

Sort them, specifying different priorities with a base:

Introduced in 2010