GROUP THEORY SYMBOL

# GTSGGetInvSubGroup

GTSGGetInvSubGroup[space group, classes, basis, index]
gives an invarian subgroup of the factor group G/T (G being a space group, T the group of pure lattice translations) with a specified index

## DetailsDetails

• GTSGGetInvSubGroup is mainly needed within the commands GTSGGetIreps and GTSGCharacterTable. According to an argument of Zak, every space group contains an invariant sub group of index 2 or 3. The invariant subgroup is found by taking into account the following theorem: A subgroup S of the group forms an invariant subgroup if and only ifit consists of complete classes of ).
• J. Zak, J. Math. Phys, 1, 165, (1960)
• See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapters 3.2.2.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

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• We choose a monoclinic basis and the space group P21/c (#14).
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