GROUP THEORY SYMBOL

GTInvSubGroupQ

GTInvSubGroupQ[group1,group2]
gives True if the group with smaller order is an invariant subgroup of the group with larger order, and gives False otherwise.

DetailsDetails

  • 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 .
  • Elements of group1 and group2 can be of type symbol, matrix, quaternion or Euler angles (compare GTEulerAnglesQ, GTQuaternionQ and GTSymbolQ).
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 3.2.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First, load the package:

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Then run the examples:

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The order of the groups doesn't matter.

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