Generators and integrity bases for some point groups

Abstract

Several results concerning the generators of point groups are discussed. The rank of C_3h, D₃ and other point groups is investigated by showing their Cayley diagrams to be isomorphic to directed planar lattices on the surface of a torus. The concept of an integrity basis for the algebra of invariants of a point group is introduced, and the construction of such a basis for the groups C_2v, C_3v and O_h is investigated in detail.