GroupTheory`
GroupTheory`

GTAbelianQ

GTAbelianQ[group]

gives True if group is an abelian group, and gives False otherwise.

Details and Options

  • If a set satisfies the four group axioms and the commutative law for the group multiplication operation, then is called "Abelian" group.
  • The group elements can be of type symbols, matrices, quaternions or Euler angles (compare GTSymbolQ, GTQuaternionQ and GTEulerAnglesQ).
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 2.1.

Examples

Basic Examples  (1)

First, load the package:

For example, is an Abelian group.

With symbolic expression:

With quaternionic expression:

With Euler Angles: