JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 32-36.doi: 10.6040/j.issn.1671-9352.0.2025.014

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The influence of subnormal subgroups on the n-solvability of groups

BAI Yiman1, HAI Jinke1,2*   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
    2. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Published:2025-11-11

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Abstract: Let n be an integer(positive or negative or 0). In this paper, we prove that the group 〈H,K〉 generated by two finite n-soluble groups H and K is still a finite n-soluble group if one of the subgroups is subnormal. Moreover, it is proved that if all non-n-nilpotent proper subgroups of a finite group G are subnormal and n-soluble, then G is n-soluble.

Key words: n-soluble group, subnormal subgroup, normal closure

CLC Number: 

  • O152.1
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[1] MA Xiaojian, MAO Yuemei. Discussion on the number of non σ-subnormal subgroups in finite groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 9-12.
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