Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 74, No. 3, pp. 943-953, 2024

A note on the $\Pi$-property of some subgroups of finite groups

Zhengtian Qiu, Guiyun Chen, Jianjun Liu

Received June 7, 2024. Published online September 16, 2024.

Abstract: Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies the $\Pi$-property in $G$ if for any chief factor $L / K$ of $G$, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $\pi(HK/K\cap L/K)$-number. We obtain some criteria for the $p$-supersolubility or $p$-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $\Pi$-property.

Keywords: finite group; $p$-supersoluble group; $p$-nilpotent group; the $\Pi$-property

Classification MSC: 20D10, 20D20

DOI: 10.21136/CMJ.2024.0226-24

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Zhengtian Qiu, Guiyun Chen, Jianjun Liu (corresponding author), School of Mathematics and Statistics, Southwest University, Beibei District, Chongqing 400715, P. R. China, e-mail: qztqzt506@163.com, gychen1963@163.com, liujj198123@163.com

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