JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 13-19.doi: 10.6040/j.issn.1671-9352.0.2023.469

• Group Theory • Previous Articles    

Action on p-groups and p-supersolvability

BAI Pengfei, WANG Junxin*, CAO Jianji   

  1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China
  • Published:2025-05-19

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Abstract: Let a finite group A act on a finite p-group P with |P|>pe≥p3, where e is a fixed positive integer. In this paper, it is proved that if every non-cyclic and non-maximal class subgroup of order pe of P is O p(A)-invariant, then O p(AAp-1) acts trivially on P(namely CP(O p(AAp-1))=P), where Ap-1 is a formation which consists of all abelian groups with exponent dividing p-1 and AAp-1 is the Ap-1-residue of A. Some sufficient conditions for a finite group to be p-supersolvable are also given.

Key words: non-cyclic and non-maximal class p-group, p-supersolvability, S-semipermutable, Zπ-permutability

CLC Number: 

  • O152
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