Journal of University of Science and Technology of China ›› 2020, Vol. 50 ›› Issue (4): 409-417.DOI: 10.3969/j.issn.0253-2778.2020.04.004

• Original Paper • Previous Articles     Next Articles

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).

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

CLC Number: