| 初等交换$p$群被内交换$p$群的中心扩张 |
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| 引用本文： | 安立坚,杨乐. 初等交换$p$群被内交换$p$群的中心扩张[J]. 数学研究及应用, 2016, 36(4): 457-466 |
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| 作者姓名： | 安立坚 杨乐 |
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| 作者单位： | 山西师范大学数学与计算机科学学院, 山西 临汾 041004,山西师范大学数学与计算机科学学院, 山西 临汾 041004 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11371232; 11471198). |
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| 摘 要： | Assume that N, F and G are groups. If there exsits a normal subgroup of G such that≌ G and G/≌ F, then G is called a central extension of N by F. In this paper, the central extension of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group of order p~3. Together with our previous work, all central extensions of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group.
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| 关 键 词： | central extension minimal non-abelian p-groups congruent |
| 收稿时间： | 2015-10-26 |
| 修稿时间： | 2016-03-18 |
The Central Extension of an Elementary Abelian $p$-Group by a Miniaml Non-Abelian $p$-Group |
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| Lijian AN and Le YANG. The Central Extension of an Elementary Abelian $p$-Group by a Miniaml Non-Abelian $p$-Group[J]. Journal of Mathematical Research with Applications, 2016, 36(4): 457-466 |
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| Authors: | Lijian AN and Le YANG |
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| Affiliation: | Department of Mathematics, Shanxi Normal University, Shanxi 041004, P. R. China and Department of Mathematics, Shanxi Normal University, Shanxi 041004, P. R. China |
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| Abstract: | Assume that $N$, $F$ and $G$ are groups. If there exsits $tilde{N}$, a normal subgroup of $G$ such that $tilde{N}cong G$ and $G/tilde{N}cong F$, then $G$ is called a central extension of $N$ by $F$. In this paper, the central extension of $N$ by a minimal non-abelian $p$-group is determined, where $N$ is an elementary abelian $p$-group of order $p^3$. Together with our previous work, all central extensions of $N$ by a minimal non-abelian $p$-group is determined, where $N$ is an elementary abelian $p$-group. |
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| Keywords: | central extension minimal non-abelian $p$-groups congruent |
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