| 摘要: |
| 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. |
| 关键词: 有限群 半次覆盖远离子群 极大子群 可解 |
| DOI： |
| 分类号:O152.1 |
| 基金项目:国家自然科学基金青年项目资助（11501176）；河南省高等学校重点科研项目资助（16A110039）. |
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| SEMI-SUBNORMAL-COVER-AVOIDANCE SUBGROUPS AND THE SOLVABLITY OF FINITE GROUPS |
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LI Shi-heng1, LIU Hai-ping2, LIU Dong-hua3
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1.School of Science, Zhengzhou University of Aeronautics, Zhengzhou 450015, China;2.School of Economics and Trade, Zhengzhou University of Aeronautics, Zhengzhou 450015, China;3.Department of Public Education, Zhengzhou Railway Vocational and Technical College, Zhengzhou 450052, China
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| Abstract: |
| 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]. |
| Key words: finite group Semi-subnormal-cover-avoidance subgroups maximal subgroups solvable |
