有限群的m-S-可补子群

doi:10.6040/j.issn.1671-9352.0.2020.399

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (4): 8-13.doi: 10.6040/j.issn.1671-9352.0.2020.399

• • 上一篇

有限群的m-S-可补子群

刘鑫,吴珍凤^*,杨南迎

江南大学理学院, 江苏无锡 214122

发布日期:2021-04-13
作者简介:刘鑫(1996— ),女,硕士研究生,研究方向为群论. E-mail:6181202006@stu.jiangnan.edu.cn*通信作者简介:吴珍凤(1991— ),女,讲师,研究方向为群论. E-mail:zhfwu@mail.ustc.edu.cn
基金资助:
国家自然科学基金资助项目(11771409)

Finite groups with some m-S-supplemented subgroups

LIU Xin, WU Zhen-feng^*, YANG Nan-ying

School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China

Published:2021-04-13

摘要/Abstract

摘要： 令G是一个有限群。群G的子群S称为在G中是m-S-置换的,如果存在着G的模子群A和S-置换子群B使得S=〈A,B〉。群G的子群H称为在G中是m-S-可补的,如果存在着G的m-S-置换子群S和G的子群T使得G=HT且H∩T≤S≤H。通过研究m-S-可补子群对有限群结构的影响,得到了有限群的p-幂零性和超可解性的一些新的判别准则,并推广了一些已得到的结果。

关键词: 有限群, 模子群, S-置换子群, m-S-置换子群, m-S-可补子群

Abstract: Let G be a finite group. A subgroup S of G is said to be m-S-permutable in G, if S=〈A,B〉 for some modular subgroup A and S-permutable subgroup B of G. A subgroup H of G is said to be m-S-supplemented in G, if there are an m-S-permutable subgroup S and a subgroup T of G such that G=HT and H∩T≤S≤H. By using the m-S-supplemented subgroups to characterize the structure of finite groups. Some new characterizations of p-nilpotency and supersolubility of finite groups are obtained and generalize some known results.

Key words: finite group, modular subgroup, S-permutable subgroup, m-S-permutable subgroup, m-S-supplemented subgroup

中图分类号:

O152

刘鑫,吴珍凤,杨南迎. 有限群的m-S-可补子群[J]. 《山东大学学报(理学版)》, 2021, 56(4): 8-13.

LIU Xin, WU Zhen-feng, YANG Nan-ying. Finite groups with some m-S-supplemented subgroups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 8-13.

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有限群的m-S-可补子群

Finite groups with some m-S-supplemented subgroups

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