| 群的融合自由积的fnFrattini子群和fcFrattini子群 |
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| 引用本文： | 邓理平,邢世奇,张志让.群的融合自由积的fnFrattini子群和fcFrattini子群[J].成都信息工程学院学报,2011,26(3):335-337. |
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| 作者姓名： | 邓理平 邢世奇 张志让 |
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| 作者单位： | 成都信息工程学院数学学院,四川成都,610225 |
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| 基金项目： | 国家自然科学基金资助项目(11071229) |
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| 摘 要： | 针对Azarian推广的任意多个子群的带循环融合自由积的Frattini子群的定理,提出了相应的关于fn-Frattini子群和fcFrattini子群的定理,并且从两个不同角度证明了结果。其中fnFrattini子群和fcFrattini子群分别定义为群的所有具有有限指数的极大正规子群的交和所有具有有限指数的极大特征子群的交,分别等于群的fn-非生成元和fc-非生成元组成的集合。进一步推广了Azarian和郭钦等相关定理。
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| 关 键 词： | 无限群论 fnFrattini子群 fcFrattini子群 fn-非生成元 fc-非生成元 群的融合自由积 |
fnFrattini Subgroups and fcFrattini Subgroups of Amalgamated Free Products of Groups |
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| DENG Li-ping
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XING Shi-qi
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ZHANG Zhi-rang.fnFrattini Subgroups and fcFrattini Subgroups of Amalgamated Free Products of Groups[J].Journal of Chengdu University of Information Technology,2011,26(3):335-337. |
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| Authors: | DENG Li-ping XING Shi-qi ZHANG Zhi-rang |
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| Institution: | (School of Mathematics,Chengdu University of Information Technology,Chengdu 610225,China) |
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| Abstract: | Based on the theorem about Frattini subgroups of the free products of any set of subgroups with a cyclic a- malgamated subgroup generalized by M. K. Azarian, the corresponding theorems on fnFrattini subgroups and fcFrattini subgroups are proposed and are proved from two different points of view in this paper. Here fnFrattini subgroups and fcFrattini subgroups are defined as the intersection of all maximal normal subgroups and the intersection of all characteristic subgroups respectively and they coincide with the set of fn-nongenerators and the set of fcnongenerators respectively. This is a further generalization of the results of M. K. Azarian and Q. Guo. |
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| Keywords: | the theory of infinite groups fn Frattini subgroups fc Frattini subgroups fn-nongenerators fc-nongenerators amalgamated free products of groups |
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