中心以外的非循环子群自正规化的有限群  

Finite groups with some non-cyclic subgroups outside centre being self-normalizing

作　　者：钟祥贵[1] 张晓蕾[1] Zhong Xianggui Zhang Xiaolei(College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China)

机构地区：[1]广西师范大学数学与统计学院

出　　处：《湖南文理学院学报（自然科学版）》2016年第4期1-3,共3页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：国家自然科学基金项目(11261007);广西省自然科学基金项目(2014GXNSFAA118009);广西高校科学技术研究项目(ZD2014016)

摘　　要：利用中心以外的非循环子群自正规化性质,刻画了有限群的结构,得到:如果对于有限群G的每个素数幂阶非循环子群H,或者H≤Z(G),或者|N_G(H):H|≤2,则G是超可解群。对于任意非循环非中心子群H满足N_G(H)=H的有限群G,给出了它的结构分类。By some non-cyclic subgroups outside centre being self-normalizing to characterize the structure of finitegroups, the results were obtained as follows： A finite group G is always supersolvable if either ｜NG（H） ： H｜ ≤ 2 orH ≤ Z（G） for every non-cyclic subgroup H of G of prime-power order. Also, finite groups G with all non-cyclicsubgroups being self-normalizing or contained in Z（G） are completely classified.

关 键 词：有限群 非循环子群 指数 正规化子 

分 类 号：O152.1[理学—数学]