Group Operations

The first section deals with a special class of finite groups which have significance far beyond group theory: groups of permutations. In the two following sections, what we have been doing so far is formalized: We have so far understood a group as a set of isometries of an object. This is clarified and generalized. Groups “operate” or “act” on sets. For example, the group of the plane operates on (the set of points of) the plane.