| 一类无限群中局部幂零性的判定准则 |
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| 引用本文： | 张志让.一类无限群中局部幂零性的判定准则[J].数学年刊A辑(中文版),2004(2). |
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| 作者姓名： | 张志让 |
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| 作者单位： | 成都信息工程学院 成都 |
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| 基金项目： | 国家自然科学基金(No.19771013)，四川省应用基础研究(No.03JY029—020)资助的项目. |
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| 摘 要： | 设G是任意群,群G的Frattini子群nat(G)定义为G的所有极大子群的交.类似地,群G的另外两个特征子群nFrat(G)及R(G)分别定义为群G的所有极大正规子群及群G的所有正规的极大子群的交.本文通过对nat(G),nnat(G)及R(G)的相互包含关系的研究,得到CF-群或中心由多重循环群的扩张群中局部幂零性的一个判定准则.同时也讨论了在某些群类中若干种广义幂零性的等价性.
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| 关 键 词： | FC-群 CF-群 中心由多重循环群的扩张群 局部幂零性 超限下中心性 Frattini子群 |
A CRITERION FOR LOCAL NILPOTENCE IN A CLASS OF INFINITE GROUPS |
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| ZHANG Zhirang Chengdu University of Information Technology,Chengdu ,China..A CRITERION FOR LOCAL NILPOTENCE IN A CLASS OF INFINITE GROUPS[J].Chinese Annals of Mathematics,2004(2). |
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| Authors: | ZHANG Zhirang Chengdu University of Information Technology Chengdu China |
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| Institution: | ZHANG Zhirang Chengdu University of Information Technology,Chengdu 610041,China. |
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| Abstract: | For any group G, the Frattini subgroup Frat(G) is the intersection of the maximal subgroups of G. In this article a criterion for local nilpotence of central-by- (finite or polycyclic) groups is established by the investigation of mutual containments of Frat(G) and two other Frattini-like subgroups, nFrat(G) and -R(G) which are denned as the intersections of the maximal normal subgroups and normal maximal subgroups, respectively. Also equivalences of generalized nilpotences are discussed in some classes of groups. |
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| Keywords: | Central-by-(finite or poly cyclic) groups FC-groups Local nilpo-tence Hypocentrality Prattini subgroup |
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