JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 67-71.doi: 10.6040/j.issn.1671-9352.0.2021.505

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Influence of σ-embedding system of subgroups on the structure of finite groups

MA Xiao-jian, MAO Yue-mei*   

  1. Institute of Quantum Information Science, Shanxi Datong University, Datong 037009, Shanxi, China
  • Online:2022-02-20 Published:2022-01-07

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Abstract: Let ∑={G0≤G1≤…≤Gn-1≤Gn} be a subgroup series of G. A subgroup H of G is said to be ∑-σ-embedded in G if H either covers or avoids every σ-abnormal pair (K,L)such that Gi-1≤Ki for some i. The influence of ∑-σ-embedded subgroups on the structure of finite groups G is studied. Some new conclusions of σ-supersoluble and σ-soluble will be given by using some related theories of σ-solvable groups, properties of complete Hall σ-set and some basic methods of finite group theory.

Key words: σ-abnormal pair, ∑, -σ-embedded subgroups, Hall σi-subgroups, σ-supersoluble, σ-soluble

CLC Number: 

  • O152.1
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