王俊新,郭秀云.半覆盖远离性质与有限群的结构[J].数学研究及应用,2010,30(3):527~535 |
半覆盖远离性质与有限群的结构 |
Semi-Cover-Avoiding Properties and the Structure of Finite Groups |
投稿时间:2008-06-30 修订日期:2009-06-30 |
DOI:10.3770/j.issn:1000-341X.2010.03.017 |
中文关键词: 极大子群 $\pi$-覆盖远离性质 $\pi$-可解群. |
英文关键词:maximal subgroup semi $\pi$-cover-avoiding property $\pi$-solvable group. |
基金项目:国家自然科学基金(Grant No.10771132);山西省高校科技项目(Grant No.20081022),山西财经大学学院科研创新团队资助项目. |
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中文摘要: |
本文定义和研究了子群的半$\pi$-覆盖远离性质,并利用该性质刻划了有限群的$\pi$-可解性.其他若干关于某些子群的半覆盖远离性与有限群结构的关系定理也被得到. |
英文摘要: |
In this paper, the so-called $\pi$-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the $\pi$-solvability of finite groups. Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group. |
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