A note on the Π -property of some subgroups of finite groups

Zhengtian Qiu; Guiyun Chen; Jianjun Liu

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 943-953
  • ISSN: 0011-4642

Abstract

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Let H be a subgroup of a finite group G . We say that H satisfies the Π -property in G if for any chief factor L / K of G , | G / K : N G / K ( H K / K ∩ L / K ) | is a π ( H K / K ∩ 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 Π -property.

How to cite

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Qiu, Zhengtian, Chen, Guiyun, and Liu, Jianjun. "A note on the $\Pi $-property of some subgroups of finite groups." Czechoslovak Mathematical Journal 74.3 (2024): 943-953. <http://eudml.org/doc/299315>.

@article{Qiu2024,
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.},
author = {Qiu, Zhengtian, Chen, Guiyun, Liu, Jianjun},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite group; $p$-supersoluble group; $p$-nilpotent group; the $\Pi $-property},
language = {eng},
number = {3},
pages = {943-953},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the $\Pi $-property of some subgroups of finite groups},
url = {http://eudml.org/doc/299315},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Qiu, Zhengtian
AU - Chen, Guiyun
AU - Liu, Jianjun
TI - A note on the $\Pi $-property of some subgroups of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 943
EP - 953
AB - 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.
LA - eng
KW - finite group; $p$-supersoluble group; $p$-nilpotent group; the $\Pi $-property
UR - http://eudml.org/doc/299315
ER -

References

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