chapter  18
12 Pages

Real Characters

WithVictor E. Hill, Thomas T. Read

The character table we worked out for D 4 at the end of Chapter 14, as well as those we worked out in Examples 15.9, 15.10, 15.11, and 15.12 contained only real numbers, in fact, integers. You know, from the one-dimensional representations of finite cyclic groups in Proposition 13.1 and of finite abelian groups in 13.6 through 13.12, that complex values may occur in characters. In this chapter We’ll see under what circumstances we may or may not expect the characters of a group to take on only real values.