| 李样明,赵立博.有限CN-群与有限c-可补群*[J].数学年刊A辑,2021,42(4):379~392 |
| 有限CN-群与有限c-可补群* |
| On Finite CN-Groups and Finite c-Supplemented Groups |
| Received:March 06, 2020 Revised:April 12, 2021 |
| DOI：10.16205/j.cnki.cama.2021.0029 |
| 中文关键词: 有限群, c-正规子群, CN-群, c-可补子群, c-可补群 |
| 英文关键词:Finite group, C-normal subgroup, CN-group, C-supplemented subgroup, C-supplemented group |
| 基金项目:国家自然科学基金(No.12071092, No.12101135),广东省基础研究及应用研究重大项目(No.2017KZDXM058),广州市科技计划项目(No.201804010088)和广东省普通高校特色创新类项目(No.2020KTSCX093) |
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| 中文摘要: |
| 有限群G的子群H称为G的c-可补子群(c-正规子群),如果存在G的子群(正规子群)N, 使得 G = NH 且 N\cap H \leq H_G,这里 H_G =\bigcap\limits_g\in G H^g 是 H 在 G 中的核.每个子群都c-可补(c-正规)的有限群称为有限c-可补群(CN-群).本文研究有限CN-群与有限c-可补群, 获得了CN- 群与c-可补群的一些新的结果.特别地, 在方法上有一定的创新, 完善近期关于CN-群的研究. |
| 英文摘要: |
| A subgroup H of finite group G is called a c-supplemented subgroup (c-normal subgroup ) of G if there exists a subgroup (normal subgroup ) N such that G = NH and N ∩H 6 HG, where HG = T g∈G Hg is the core of H in G. A finite group with every subgroup c-supplemented (c-normal) is called a finite c-supplemented group(CN- group). In this paper,many new characterizations of c-supplemented group were obtained. In particular, some methodological innovations have been made to improve the studies of the CN-group. |
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