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
李娜 1史江涛2
作者信息
- 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
- 折叠
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.
Abstract
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Key words
non-metacyclic subgroup/self-centralizing/TI-subgroup/subnormal subgroup/solvable引用本文复制引用
基金项目
国家自然科学基金(11761079)
山东省自然科学基金(ZR2017MA022)
出版年
2024
NETL
NSTL
万方数据