A Proof for the Existence of Five Stereogenicity Types on the Basis of the Existence of Five Types of Subgroups of RS-Stereoisomeric Groups. Hierarchy of Groups for Restructuring Stereochemistry (Part 3)

A proof for the existence of five stereogenicity types, which has once been demonstrated intuitively by means of stereoisograms, is mathematically given on the basis of the five factor groups derived from RS-stereoisomeric groups. These factor groups are proved to correspond to five types of subgroups appearing in RS-stereoisomeric groups. Thereby, the relationship between the concept of chirality and the concept of stereogenicity is clarified after the latter concept is replaced by a more specified concept, i.e., RS-stereogenicity. Moreover, the concepts of holantimers and RS-diastereomers gain a sound mathematical basis.