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.
作者
刘文静
史江涛
LIU Wenjing;SHI Jiangtao(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)
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)。
