Primitive Inducing Degrees Of Characters

Given a finite group G and x? Irr(G),we call a character pair(H,?)an inducing pair of x if x=?G and call ?(1)an inducing degree of x.Let MDI(x)be the set of minimal members in the set of inducing degrees of x under the divisibility of numbers.Let T be a triple and ?' be a subtriple of ?.We say that ?' is a linear limit of T if it is a multilinear reduction of T such that the only possible linear reduction of ?' is ?' itself.In this thesis,we prove that a triple and its every linear limit have the same set of minimal induced degrees.This strengthens Dade's theorem and several applications are given.The main conclusions of this thesis are as followsTheorem A Let T be a triple.If ?' is a linear limit of ?,for any x ? Irr(T),assume x'?Irr(?')is a inductive correspondence of X,then MDI(x)=MDI(x').As applications,we prove that any two linear limits of a triple have the same degree Theorem B Let T be a triple.If ?'and ?" are linear limits of ?,then degT'=degT".