中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (4): 409-417.DOI: 10.3969/j.issn.0253-2778.2020.04.004

• 论著 • 上一篇    下一篇

两个σ-超可解子群的积

毛月梅,马小箭   

  1. 山西大同大学数学与统计学院,山西大同 037009
  • 收稿日期:2020-03-12 修回日期:2020-04-15 接受日期:2020-04-15 出版日期:2020-04-30 发布日期:2020-04-15

The product of two σ-supersoluble groups

  1. MAO Yuemei, MA Xiaojian
  • Received:2020-03-12 Revised:2020-04-15 Accepted:2020-04-15 Online:2020-04-30 Published:2020-04-15
  • Contact: MAO Yuemei
  • About author:MAO Yuemei(corresponding author),female, born in 1979, PhD/ associated Prof. Research field: Theory of groups.E-mail:maoyuemei@126.com
  • Supported by:
    Supported by Youth Program of National Natural Science Foundation of China (11901364), Applied Basic Research Program Project of Shanxi Province (201901D211439), Applied Basic Research Project of Datong City (2019156), Science and Technology Innovation Project of Shanxi Province (2019L0747).

摘要: 设Nσ是指所有σ-幂零群所有构成的群类,并记GNσ是G的σ-幂零群上根.我们称群G是σ-超可解的,如果G的含于GNσ的主因子是循环的.群G的子群H称为与子群T是完全c-置换的,如果存在元素x∈〈H,T〉满足HTx= TxH.利用子群的完全c-置换性研究两个σ-超可解群的积所构成的有限群的结构.

关键词: 有限群, σ-幂零群, σ-超可解群, σ-次正规, 完全c-置换

Abstract: Let Nσ denote the classes of all σ-nilpotent groups and GNσ be the σ-nilpotent residual of G. We say that G is σ-supersoluble if each chief factor of G below GNσ is cyclic. A subgroup H of G is said to be completely c-permutable with a subgroup T of G if there exists an element x∈〈H,T〉 such that HTx=TxH.

Key words: finite groups, σ-nilpotent groups, σ-supersoluble groups, σ-subnormal, completely c-permutable

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