Primitive Inducing Degrees Of Characters

Given a finite group G and x∈ Irr(G),we call a character pair(H,θ)an inducing pair of x if x=θG and call θ(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 τ’ be a subtriple of τ.We say that τ’ is a linear limit of T if it is a multilinear reduction of T such that the only possible linear reduction of τ’ is τ’ 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 τ’ is a linear limit of τ,for any x ∈ Irr(T),assume x’∈Irr(τ’)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 τ’and τ" are linear limits of τ,then degT’=degT".