不可约特征标和B_π-特征标的对应关系

Correspondent Relationships of Irreducible Characters and B_π-Characters

首先给出 Isaacs著名引理的一个推广 .把其中关于θ和φ分别为 G -不变的和 K -不变的特征标的条件减弱为更为一般的和常见的惯性群关系 IK(θ) =IK(φ) .其次 ,我们证明了当θ为 N的一个 Bπ特征标而φ恰为一个与θ相伴的 Fong特征标时 ,相应的对应关系自动成为 Bπ-特征标和 Fong特征标的对应 .

We first give an expansion of Isaacs famous Lemma 4 1. Among it characteristic condition of θ and separately being invariant in G and K weakens general and ordinary relationship: I K(θ)=I K(φ). Secondly, we have proved that when there exists θ∈B π(N), and φ is a Fong character associated with θ, the correspondence relationship automatically becomes the correspondence of B π- character and Fong character.