In this final chapter, we explore the character theory of finite groups. Section 14 introduces characters and develops some of their elementary properties. This development is continued in Section 15 with the introduction of the character table and the verification of the orthogonality relations. The bulk of this section is devoted to a series of instructive examples involving the computation of character tables. In Section 16, we momentarily return to a more general setting with the definition of induced modules; we then study induced characters, finishing with a well-known group-theoretic theorem of Frobenius that (at present) cannot be established without invoking character theory.
Unable to display preview. Download preview PDF.