非次正规的非交换的非TI-子群的个数不超过21的非可解群  

On Non-Solvable Groups Having at Most 21 Non-Subnormal Non-Abelian Non-TI-Subgroups

作　　者：刘文静 史江涛[1] LIU Wenjing;SHI Jiangtao(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2024年第1期12-15,共4页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11761079);山东省自然科学基金资助项目(ZR2017MA022,ZR2020MA044)。

摘　　要：为了进一步研究非TI-子群的个数对有限群可解性的影响,先考察非交换的非TI?子群,证明了如果非可解群G的非交换的非TI?子群的个数不超过21,则G同构于交错群A5。进而考察非次正规的非交换的非TI-子群的个数,证明了如果非可解群G的非次正规的非交换的非TI?子群的个数不超过21,则亦有G同构于A5。In order to give a further study of the influence of the number of non-TI-subgroups on the solvability of fi-nite groups,we first investigate non-abelian non-TI-subgroups and prove that if G is a non-solvable group having at most 21 non-abelian non-TI-subgroups,G is isomorphic to the alternating group A5.Moreover,we investigate non-subnormal non-abelian non-TI-subgroups and we also have that G is isomorphic to A5 if G is a non-solvable group having at most 21 non-subnormal non-abelian non-TI-subgroups.

关 键 词：非可解群 非次正规 非交换的非TI-子群 

分 类 号：O152.1[理学—数学]