| Semi-Cover-Avoiding Properties and the Structure of Finite Groups |
| Received:June 30, 2008 Revised:June 30, 2009 |
| Key Words:
maximal subgroup semi $\pi$-cover-avoiding property $\pi$-solvable group.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10771132), the Science and Technology Foundation of Shanxi Province for Colleges (Grant No.20081022) and the Team Innovation Research Foundation of Shanxi University of Finance and Economics. |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.03.017 |
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