GROUP THEORY SYMBOL

GTGetSubGroups

GTGetSubGroups[group]
gives all subgroups of a group.

DetailsDetails

  • 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:
  • GOGroupOrder1Sets 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

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First, load the package:

In[1]:=
Click for copyable input

Calculate the subgroups of

In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Options  (3)Options  (3)

Top