关于某些不可约特征标的核和拟核

On the Ker and the Quasikernel of some Irreducible Characters

作者建立下述两个主要结果:(i)令G是有限非Abel群,N G.设n是固定的正整数,Kn(N)≠{1}(其中Kn(N)是N的下中心列的第n+1项),Irr(G|Kn(N))中的每个非线性的monolithic特征标的次数都被p整除,则N是p-幂零的和可解的;(ii)令G是个有限非Abel群,N G.设n是固定的正整数,Kn(N)≠{1},Irr(G|Kn(N))中的每个非线性的monolithic特征标的次数不被p整除,则N有正规Abel的Sylowp-子群.利用这两个结果,作者改进了关于核和拟核及p-闭群的某些结果.

The authors establish two main results as follows： （i） Let N Δ← G , n be a fixed positive integer. denote the n ＋ 1 term of the lown central serries of N by Kn （N）. Suppose that the degree of every monolithic character in Irr（G｜Kn （N））is divisible by p, then N is p-nilpotent and solvable; （ii） Let NΔ← G, n be a fixed positive integer. Suppose that the degree of every monolithic character in Irr（ G ｜ Kn （N） ） is not divisible by p, then N is p-closed with abelian Sylow p-subgroup. By using the two theorems, some results about the kernels and quasikernels of some irredusible characters are obtained.