Primitive Period Isometric Transformations and the Longuet-Higgins Group

3 Primitive Period Isometric Transformations and the Longuet-Higgins Group 

It is of interest to point out the role of primitive period isometric transformations (cf. Sect. 2.2.2.) in both the isometric and the Longuet-Higgins groug. According to Eq. (2.41) this type of transformations is represented on the basis X ( ) by 

Considering now the action of primitive period isometric operators on the basis Xk(e, ), we will distinguish between the following cases 

This shows that the representation of the group on the nuclear position vectors referred to the laboratory fjxed coordinate system is not a faithful representation of the isometric group ( ) = r NCf. W  

Therefore, SRMs with ( ) = Cj, for which the permutation-inversion group is always isomorphic to r(NCl) J the relation between SfSt and the isometric group ( ) is only a homomorphism 

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