A2 Class algebra

Because binary composition is unique, the classes of G are all disjoint, with no elements in common. For example, the classes of the permutation group S3 are (- = P0, Z 2 Pi P2, 3 = P3 P4 P5 (see Section 1.2). The Dirac character fl of a class (sometimes called the class sum ) is the sum of the elements in a class 

The inverse class of written Z-, is the set of elements of G that are the inverses of the 

It follows from the definition of the inverse class that the mapping — Z- is isomorphous, 

Exercise A2.1-1 Show that if g, C then 9 1 form a class with 9 = 9. 

Since binary composition is unique, as / 1,2,. .., cj with the same gh a different element 

---