Minimal splitting fields in cyclotomic extensions

Abstract

Suppose G G is a finite group of exponent n n and X X an irreducible character of G G . In this note we give sufficient conditions for the existence of a minimal degree splitting field L L with Q ( X ) ⊆ L ⊆ Q ( ζ n ) Q(X) \subseteq L \subseteq Q({\zeta _n}) .