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.
作者
李娜
史江涛
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)
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).
关键词
非亚循环子群
自中心
TI-子群
次正规子群
可解
non-metacyclic subgroup
self-centralizing
TI-subgroup
subnormal subgroup
solvable
