chapter  2
9 Pages

Groups and Subgroups

WithVictor E. Hill, Thomas T. Read

Many mathematical concepts, such as that of a group, are generalized from a variety of specific examples; the three examples presented in the text of Chapter 1, together with those in Exercises 1.3 through 1.8, illustrate this principle. The reason that we are interested in studying groups is that a great many apparently diverse examples have certain features in common that, when abstracted, allow us to study all or some of the examples at once in a general theory. Moreover, group theory has a variety of applications in the physical sciences, which one may explore by using knowledge of the general theory.