GroupTheory`
GroupTheory`

GTSubGroupQ

GTSubGroupQ[group1,group2]

gives True if the group with smaller order is a subgroup of the group with larger order, and gives False otherwise.

Details and Options

  • A subset of a group is called "subgroup" if satisfies the four group axioms with the same multiplication operation as .
  • The elements of group1 and group2 can be of type symbol, matrix, quaternion or Euler angles (compare GTEulerAnglesQ, GTQuaternionQ and GTSymbolQ).
  • GOFast GOFastValueOptional 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:

is a subgroup of

The order of the groups doesn't matter.

Options  (2)

GOFast  (2)

The evaluation time can be significantly decreased, using GOFastTrue.

If GOFastFalse is used,the input is validated.