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| 中心以外的非循环子群自正规化的有限群 | |
| 引用本文： | 钟祥贵,张晓蕾. 中心以外的非循环子群自正规化的有限群[J]. 湖南文理学院学报(自然科学版), 2016, 28(4): 1-3. DOI: 10.3969/j.issn.1672-6146.2016.04.001 |
| 作者姓名： | 钟祥贵 张晓蕾 |
| 作者单位： | 广西师范大学 数学与统计学院，广西 桂林，541004;广西师范大学 数学与统计学院，广西 桂林，541004 |
| 基金项目： | 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。 |
| 关 键 词： | 有限群 非循环子群 指数 正规化子 |
Finite groups with some non-cyclic subgroups outside centre being self-normalizing |
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| Zhong Xianggui,Zhang Xiaolei. Finite groups with some non-cyclic subgroups outside centre being self-normalizing[J]. Journal of Hunan University of Arts and Science:Natural Science Edition, 2016, 28(4): 1-3. DOI: 10.3969/j.issn.1672-6146.2016.04.001 | |
| Authors: | Zhong Xianggui Zhang Xiaolei |
| Abstract: | By some non-cyclic subgroups outside centre being self-normalizing to characterize the structure of finite groups, the results were obtained as follows:A finite group G is always supersolvable if either|NG(H):H| ≤ 2 or H ≤ Z(G) for every non-cyclic subgroup H of G of prime-power order. Also, finite groups G with all non-cyclic subgroups being self-normalizing or contained in Z(G) are completely classified. |
| Keywords: | finite groups non-cyclic subgroup index normalize |
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