Microcomputer‐aided instruction and research in group theory

Abstract

AbstractA collection of programs which aid in the use of group theory has been developed for the Apple II. The programs automate much of the tedious algebra necessary to generate character tables and representation matrices from the properties of the operators chosen to generate the group. At the same time, the presentation of intermediate results provides a schematic guide to the procedures by which groups are constructed. The choice of generators is not limited to the reflections, rotations, and inversions, which are the familiar features of chemical group theory. Any generator representable as a permutation may be treated; thus general permutation groups and Longuet‐Higgins groups may be studied. As an illustration we describe the states of beryllium borohydride, which require a form of Longuet‐Higgins group theory.