What is the relationship between the electron groups on an atom and the number of its pure atomic orbitals that hybridize?
The relationship is that the number of groups shows the number of hybrid orbital's formed, which equals the number of atomic orbitals mixed. The number of atomic orbitals mixed is equal to the hybridization of the element.
They need each other so as to form a molecule. Whether it be linear, tetrahedral, or planer,,etc. Its all part of the Valence Bond Theory.