Enantiomorphic orbit

More generally, if G, equipped with a sign map, acts on X in such a way that its kernel is not G, i.e. G G , then we can group the orbits of G on X into two subsets. The first one comprises of those G-orbits which are also G "-orbits. In the following picture we denote such an orbit by , and call it a self-enantiomorphic orbit since it consists of self-enantiomorphic elements x X. The second set of orbits consists of the G-orbits that split into two G -orbits. We indicate one of them by , the other one by e, and call the corresponding orbit u e an enantiomorphic orbit of G or the pair , an enantiomorphic pair of G -orbits. This union consists of elements x e X that we call enantiomorphic elements ... 

Subtracting this from the number of orbits of the rotation group we hnd - The number of enantiomorphic permutational isomers is... 

Now we suppose that the set of substituents is y = y uY, where y = 1, i.e. consists of the substituent glycine alone, while Y, consists of peiirs of enantiomorphic amino acids, so that Y j is even. As consists of four 1-cycles, while pj is the product of two 2-cycles, and similarly for pi, p2 we find the following expressions for the numbers of orbits of the point and the rotation group in this particular situation ... 

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