关于有限群的自中心的非亚循环子群的TI-性和次正规性  

On the TI-property and subnormality of self-centralizing non-metacyclic subgroups of a finite group

作　　者：李娜 史江涛[2] LI Na;SHI Jiangtao(College of Mathematics and Statistics,Zaozhuang University,Zaozhuang 277160,China;School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]枣庄学院数学与统计学院,山东枣庄277160 [2]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《纯粹数学与应用数学》2024年第2期212-217,共6页Pure and Applied Mathematics

基　　金：国家自然科学基金(11761079);山东省自然科学基金(ZR2017MA022).

摘　　要：对于自中心的非亚循环子群,本文把它们的TI-性和次正规性结合在一起证明了:如果有限群G的每个自中心的非亚循环子群皆为TI-子群或次正规子群,则G的每个非亚循环子群皆次正规于G,而且这类群是可解的.此外,本文还证明了如果有限群G的每个自中心的非亚循环子群皆为TI-子群,则G的每个自中心的非亚循环子群皆在G中正规.For self-centralizing non-metacyclic subgroups,we combine the TI-property and subnormality together to prove that if every self-centralizing non-metacyclic subgroup of a finite group G is a TI-subgroup or a subnormal subgroup,then every non-metacyclic subgroup of G is subnormal in G and such a group G is solvable.Moreover,we show that if every self-centralizing non-metacyclic subgroup of a finite group G is a TI-subgroup then every self-centralizing non-metacyclic subgroup of G is normal in G.

关 键 词：非亚循环子群 自中心 TI-子群 次正规子群 可解 

分 类 号：O152.1[理学—数学]