关于Glauberman-Isaacs特征标对映的注记

假设群A经自同构互素地作用在G上.设χ是G的一个A-不变不可约特征标,π(G,A)表示Glauberman-Isaacs特征标对映.对于B≤A,T.R.Wolf曾猜想χπ(G,A)是χπ(G,B)a的一个不可约成份,此处C=CG(A).设G=N(X)H且(|N|,|H|)=1,假定H是A-不变的且N是一个Sylow塔群,N的Sylow-子群是交换的.在本文中,我们证明了如果这个猜想对所有H的A-不变子群成立,则猜想对G也成立.

A Note on Glauberman-Isaacs Character Correspondences

Suppose that a group A acts on a group G of coprime order via automorphisms. Let χ be an A-invariant irreducible character of G and π(G, A ) denote the character correspondences. For B ≤A, T. R. Wolf once conjectured that χπ(G, A ) is an irreducible constituent of χπ(G, B )e, where C =CG (A). Let G=N (X) H be such that (|N|, |H|)= 1, suppose that H is A-invariant and N is a Sylow tower group and all of Sylow subgroups of N are abelian. In this note, we prove that if the Conjecture holds for all of A-invariant subgroups of H, then the Conjecture holds for G.