Chapter 2 - GROUP CONCEPTS

Abstract

This chapter presents the basic group definitions and concepts. A group is defined as a set, or collection, of elements that obeys the four rules, namely, product or closure, identity, inverse, and associativity. A binary operation called combination or product that describes the operation by which two members of the set combine to form a third member of the set. This product can be ordinary multiplication, addition, operation as in a symmetry operation, matrix multiplication, etc. An easy and important way to display the product of the group elements is by way of a multiplication table. In multiplication tables each element of the group appears only once in each row and in each column. Inverse of a product implies that the reciprocal of the product of several group elements is equal to the product of the reciprocals of the elements in the reverse order. A complete set of symmetry operations means that all the symmetry operations that transform a molecule into itself are included in the set.