| F-Decomposition of Noetherian Modules over Hyper-（Cyclic or Finite）Groups |
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| 引用本文： | 秦应兵,段泽勇.F-Decomposition of Noetherian Modules over Hyper-（Cyclic or Finite）Groups[J].西南交通大学学报(英文版),2004,12(1):83-86. |
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| 作者姓名： | 秦应兵 段泽勇 |
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| 作者单位： | [1]DepartmentofAppliedMathematics，SouthwestJiaotongUniversity，Chengdu610031，China [2]DepartmentofMathematics，SouthwestNormalUniversity，Chongqing400715，China |
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| 基金项目： | TheNationalNaturalScienceFoundation
ofChina (No .10 1710 74 ) |
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| 摘 要： | Let F be a locally defined formation consisting of locally soluble groups，G a hyper-(cyclic or finite)locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite，G∈F,f(∞)≌f(p)，f(P)≠Фfor each P∈π．The following conclutions are obtained：(1)if there exists a maximal submodule B of A such that A／B is F central in G and B has no nonzero F centml ZG-factors，then A has an F decomposition；(2)if there exists an irreducible F central submodule B of A such that all ZG-composition factors of A／B are F ecentric，then A has an F decomposition．
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| 关 键 词： | 群论 F-分解 Noetherian模数 最大分模数 |
F-Decomposition of Noetherian Modules over Hyper-(Cyclic or Finite) Groups |
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| Qin Yingbing,Duan Zeyong.F-Decomposition of Noetherian Modules over Hyper-(Cyclic or Finite) Groups[J].Journal of Southwest Jiaotong University,2004,12(1):83-86. |
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| Authors: | Qin Yingbing Duan Zeyong |
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| Institution: | 1. Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, China
2. Department of Mathematics, Southwest Normal University, Chongqing 400715, China |
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| Abstract: | Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition. |
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| Keywords: | Noetherian module Hyper-(cyclic or finite) group F-decomposition |
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