| 点稳定子群循环的pq2级传递置换群 |
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| 引用本文： | 张军阳. 点稳定子群循环的pq2级传递置换群[J]. 漳州师院学报, 2014, 0(3): 6-12 |
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| 作者姓名： | 张军阳 |
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| 作者单位： | 闽南师范大学数学与统计学院,福建漳州363000 |
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| 基金项目： | 福建省教育厅A类科技项目（JA14204） |
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| 摘 要： | 点稳定子循环的传递置换群在地图理论中占有重要的地位.事实上,正则的可定向地图就是由此类群刻画的.因此对此类群做些研究是十分有意义的.本文证明了点稳定子循环的pq2（p和q都是素数）级传递置换群要么可解,要么同构于A5或S5.其证明完全独立于有限单群分类定理.
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| 关 键 词： | 置换群 传递群 点稳定子 可解群 |
Transitive Permutation Groups of Degree pq2 with Cyclic Stabilizers |
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| ZHANG Jun-yang. Transitive Permutation Groups of Degree pq2 with Cyclic Stabilizers[J]. Journal of ZhangZhou Teachers College(Philosophy & Social Sciences), 2014, 0(3): 6-12 |
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| Authors: | ZHANG Jun-yang |
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| Affiliation: | ZHANG Jun-yang (School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, China) |
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| Abstract: | The transitive groups with cyclic stabilizers play an important role in map theory. Actually, regular maps can be characterized by these groups. Hence it is essential to do some researches on these groups. In this paper, it is proved that the transitive permutation groups of degree pq2 with cyclic stabilizers are solvable or isomorphic to A 5 or $5. The proof is independent of the classifications of simple groups. |
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| Keywords: | permutation group transitive group stabilizer solvable group |
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