JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 9-14.doi: 10.6040/j.issn.1671-9352.0.2023.321

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Influence of SS-quasinormal subgroups on p-nilpotence of finite groups

Jianling GAO1(),Yuemei MAO1,*(),Chenchen CAO2   

  1. 1. School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, Shanxi, China
    2. School of Mathematics and Statistics, Ningbo University, Ningbo 315211, Zhejiang, China
  • Received:2023-07-22 Online:2024-08-20 Published:2024-07-31
  • Contact: Yuemei MAO E-mail:gaojl1981@163.com;maoyuemei@126.com

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Abstract:

Let G be a finite group. A subgroup H is called SS-quasinormal in G if there is a subgroup B of G such that G=HB, and HP=PH holds for all prime p∈π(B) and P∈Sylp(B). The structures of finite groups with SS-quasinormality of primary subgroups are studied. Some new criteria of p-nilpotent group are given by using induction on the order of G and counterexample of minimal order.

Key words: SS-quasinormal subgroup, p-nilpotent group, p-supersolvable group, induction, counterexample of minimal order

CLC Number: 

  • O152.1
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