On the cycle index of point groups

Abstract

In this brief work we express the cycle index of the molecular point groups as a function of a limited number of initial geometrical parameters. Such parameters are the number $m$ of elements composing the domain D of sites of substitutions in the molecule belonging to the point group G, and the numbers $\left( {n\left( {C_n } \right),n\left( \sigma \right),...} \right)$ of sites of D lying on the symmetry elements $\left( {C_n ,\sigma ,...} \right)$ for G.