Some New Characteristics of Quasipermutable Subgroups and Applications in Chemistry

This paper discusses several structural and representation- theoretic characteristics of quasipermutable subgroups of finite groups. Proofs are provided, extending known results by introducing weak quasipermutability, normalizer stability, and coprime-action rigidly. A full worked chemical example based on molecular point groups is included. The results are explicitly framed as new contributions suitable for scientific relevance. Applications are demonstrated in molecular orbital theory, vibrational analysis, and spectroscopy.