The Action of Galois Groups on Characters of Finite Groups

Abstract

This dissertation deals with the action of Galois groups on characters of finite groups. We study the compatibility between Galois group action on the conjugacy classes and on characters of the group. We study a theorem of seigel for algebraic numbers and the relationship with field extensions. Galois correspondence is an important tool to deal with integrality as well as p-rational characters. We recover the notion of Schur index which is a topic links Galois group, irreducible characters and field extensions