GroupTheory`
GroupTheory`

GTGetInvSubGroup

GTGetInvSubGroup[grp, classes, index n]

gives an invariant subgroup of index n

Details and Options

  • A subgroup of a group is called "invariant subgroup" if for every and every .
  • A necessary and sufficient condition for being an invariant subgroup of is satisfied if consists entirely of complete classes of .
  • MaxIterations 10000Maximal number of iterations to find an invariant subgroup
    GOVerbose TrueControls the output of additional information.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 3.2.

Examples

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Basic Examples  (1)

First, load the package:

We calculate an invariant subgroup of index 2 for the point group O.

GTGetInvSubGroup can be used to construct the chief series of a solvable group.

Options  (2)

GOVerbose  (1)

Using GOVerbose it can be controlled if warnings are printed.

MaxIterations  (1)

MaxIterations controls the number of random iterations used to find an invariant subgroup.