半次覆盖远离子群和有限群的可解性
SEMI-SUBNORMAL-COVER-AVOIDANCE SUBGROUPS AND THE SOLVABLITY OF FINITE GROUPS

本文定义了有限群的半次覆盖远离子群概念，研究了半次覆盖远离子群和有限群的可解性问题.利用某些半次覆盖远离子群刻划了有限群的可解性，得到了若所有的sylow子群（或极大子群）半次覆盖远离则群可解，推广了文献[6]中的结果.
In this paper, we define semi-subnormal-cover-avoidance subgroups of finite groups and study the solvability between groups and their semi-subnormal-cover-avoidance subgroups. With semi-subnormal-cover-avoidance subgroups, we characterize the solvability of finite groups and obtain the results that the group is soluble if all of its sylow groups (or maximal subgroups) are semi-subnormal-cover-avoidance subgroups, which generalize the results in[6]