| Splitting Extensions of Abelian by Hyper-（ cyclic or finite） Groups （Ⅱ ） |
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| 引用本文： | 秦应兵. Splitting Extensions of Abelian by Hyper-（ cyclic or finite） Groups （Ⅱ ）[J]. 西南交通大学学报(英文版), 2006, 14(3): 291-294 |
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| 作者姓名： | 秦应兵 |
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| 作者单位： | Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, China |
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| 基金项目： | The Fundamental Science Foundation of Southwest Jiaotong University （ No. 2004B08） |
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| 摘 要： | Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.
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| 关 键 词： | 交换 周期 模型 共轭性 |
| 文章编号： | 1005-2429（2006）03-0291-04 |
| 收稿时间： | 2005-04-21 |
Splitting Extensions of Abelian by Hyper-(cyclic or finite) Groups ( Ⅱ ) |
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| Qin Yingbing. Splitting Extensions of Abelian by Hyper-(cyclic or finite) Groups ( Ⅱ )[J]. Journal of Southwest Jiaotong University, 2006, 14(3): 291-294 |
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| Authors: | Qin Yingbing |
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| Abstract: | Let (T*)be a locally defined formation consisting of locally solvable groups, G a hyper-(cyclic or finite) locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained: if G ∈(T*)f( ∞ ) (∪)f(p), f(p) ≠Φ for each P ∈π, and A has no nonzero (T*)-central ZG-images, then any extension E of A by G splits conjugately over A, and A has no nonzero (T*)-central ZG-factors. |
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| Keywords: | Noetherian module Abelian group Hyper-(cyclic or finite) group Splitting conjugacy Extension |
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