某些子群介于正规与反正规之间的有限群

郭鹏飞, 石化国

数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 841-848.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 841-848. DOI: 10.12386/A20210001
论文

某些子群介于正规与反正规之间的有限群

    郭鹏飞1, 石化国2
作者信息 +

Finite Groups in Which Certain Subgroups are Between Normal and Abnormal

    Peng Fei GUO1, Hua Guo SHI2
Author information +
文章历史 +

摘要

有限群G的子群H称为G的BNA子群，若对任意的x∈G有Hx=H或x∈⟨H，Hx⟩.若有限群G的所有素数阶和4阶循环子群都是G的BNA子群，则称G为CBNA群.本文主要刻画CBNA群的结构，并且给出所有真子群都是CBNA群的完全分类.

Abstract

A subgroup H of a finite group G is a BNA-subgroup of G if either Hx=H or x∈⟨H,Hx⟩ for all x∈G. A finite group G is called a CBNA-group if its all cyclic subgroups of order prime or 4 are BNA-subgroups of G. The main aim of this paper is to investigate the structure of CBNA-groups, and the groups whose all proper subgroups are CBNA-groups are classified completely.

关键词

BNA子群 / 极小子群 / 循环子群 / 超可解群 / CBNA群

Key words

BNA-subgroups / minimal subgroups / cyclic subgroups / supersolvable groups / CBNA-groups

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导出引用
郭鹏飞, 石化国. 某些子群介于正规与反正规之间的有限群. 数学学报, 2022, 65(5): 841-848 https://doi.org/10.12386/A20210001
Peng Fei GUO, Hua Guo SHI. Finite Groups in Which Certain Subgroups are Between Normal and Abnormal. Acta Mathematica Sinica, Chinese Series, 2022, 65(5): 841-848 https://doi.org/10.12386/A20210001

参考文献

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基金

国家自然科学基金资助项目（12061030，11661031）；海南省自然科学基金资助项目（119MS039）
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