| 赵立博,龚律,郭秀云.子群的核平凡或正规闭包极大的有限p群[J].数学年刊A辑,2021,42(4):419~426 |
| 子群的核平凡或正规闭包极大的有限p群 |
| Finite p-Groups with a Trivial Core or the Normal Closure Index p for Every Non-normal Abelian Subgroup |
| Received:December 09, 2019 Revised:March 29, 2021 |
| DOI：10.16205/j.cnki.cama.2021.0032 |
| 中文关键词: ACT 群, 非 Dedekind 群, 有限p 群, CC 群 |
| 英文关键词:ACT -group, Non-Dedekind group, Finite p-group, CC-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) |
| Author Name | Affiliation | | ZHAO Libo | College of Mathematics, Guangdong University of Education, Guangzhou 510310, China. | | GONG L¨u | School of Sciences, Nantong University, Nantong 226019, Jiangsu, China. | | GUO Xiuyun | Department of Mathematics, Shanghai University, Shanghai 200444, China. |
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| 中文摘要: |
| 称有限 p 群 G 为ACT 群,如果对每个交换子群H, 其正规核 HG=1 或 HG=H. 又称p 群 G是CC 群,如果对每个非正规交换子群H, 有 HG=1 或 HG 在G中的指数为 p. 本文分类了ACT 群和CC 群. |
| 英文摘要: |
| A finite p-group G is called an ACT -group if the core HG = 1 or HG = H for every abelian subgroup H. And a p-group G is called a CC-group if HG = 1 or HG = HG has index p for every non-normal abelian subgroup H. In this paper, the authors classify the ACT -groups and the CC-groups. |
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