GroupTheory`
GroupTheory`

GTGetSubGroups

GTGetSubGroups[group]

gives all subgroups of a group.

Details and Options

  • A subset of a group is called "subgroup" if satisfies the four group axioms with the same multiplication operation as . See also GTSubGroupQ
  • For large groups the execution time can be very large. It is proposed to search for subgroups of a certain order instead of trying to find all.
  • The following options can be given:
  • GOGroupOrder 1Sets the order for the subgroups
  • GOFastGOFastValueSkips the input validation
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, Chapter 3.1

Examples

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Basic Examples  (1)

First, load the package:

Calculate the subgroups of

Options  (3)

GOGroupOrder  (1)

GOFast  (2)

If GOFastFalse is used, a check of the input will be performed.

Since GTGetSubgroups can be very time consuming you won't save much by setting GOFastTrue.