Monomiality Of A Class Of Subgroups Of M-Groups

A new reduction technique of character diagrams was presented by using the Glauberman-Isaacs character correspondences and the theory of linear limits due to Dade and Loukaki.This technique was used to study the monomiality of character triples and a classical result of Dade was improved.A sufficient condition for a class of subgroups of M-groups to be monomial was obtained.The main conclusions of this paper are as follows:Theorem 1 Let J=(G,N,?)be a triple and S be a Dade subgroup of J.If L is a normal subgroup of G contained N and ??Irr(L)is S-invvarant,then J(?)(s)=J(s)(?(s)).Theorem 2 Let J=(G,N,?)be a triple and S be a Dade subgroup of J.Assume that J has a trivial linear limit.If J is monomial,then the S-correspondence J(s)=(NG(S),CN(S),?(S))is also mono,mial.Corollary 3 Let G be an M-group,N(?)G and S ?G such that(|N|,|S|)= 1 a,nd NS(?)G.Assume that J=(G,N,?)has a trivial linear limit for every ??Irr(N).Then NG(S)is an M-group.Corollary 4 Let G be an M-group,N(?)G and S ? G such that(|N|,|S|)= 1 and NS(?)G.If every Sylow subgroup of N is abelian,then NG(S)is also an M-group.