Study on Some Groups Whose Elements Are Symmetries of Geometric Objects

In this paper discuses some important examples of non-abelian groups whose elements are symmetries of geometric objects, which is called dihedral group D₂n, and uses them on some chemical compounds to understand how their atoms vibrate. As we know chemists and mineralogists study dihedral groups in order to classify the structure of molecules and crystals, respectively. Farther more, to study the vibration of atoms of some chemical compounds, we will represent them as geometrical shapes that correspond to the number and arrangement of their atoms in the molecule, with the same angle of binding.