非次正规的偶数阶非幂零真子群的个数不超过21的非可解群  

Finite Groups in Which Number of Non-Subnormal Non-Nilpotent Proper Subgroups of Even Order Is Not Greater Than

作　　者：田云凤 史江涛[1] 刘文静 TIAN Yunfeng;SHI Jiangtao;LIU Wenjing(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2期125-127,共3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);烟台大学研究生科研创新基金(GGIFYTU2312)。

摘　　要：为了进一步研究特殊子群的数量性质对有限群可解性的影响,证明了非次正规的偶数阶非幂零真子群的个数不超过21的非可解群仅有交错群A_(5)和特殊线性群SL_(2)(5)。As a further study of the influence of quantitative property of special subgroups on the solvability of finite groups,we prove that if a non-solvable group G has at most 21 non-subnormal non-nilpotent subgroups of even order,G must be isomorphic to the alternating group A_(5)or the special linear group SL_(2)(5).

关 键 词：偶数阶 非幂零真子群 可解群 非可解群 

分 类 号：O152.1[理学—数学]