On Π -property of some maximal subgroups of Sylow subgroups of finite groups

Zhengtian Qiu; Jianjun Liu; Guiyun Chen

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 4, page 1349-1358
  • 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 study the influence of some p -subgroups of G satisfying the Π -property on the structure of G , and generalize some known results.

How to cite

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Qiu, Zhengtian, Liu, Jianjun, and Chen, Guiyun. "On $\Pi $-property of some maximal subgroups of Sylow subgroups of finite groups." Czechoslovak Mathematical Journal 73.4 (2023): 1349-1358. <http://eudml.org/doc/299576>.

@article{Qiu2023,
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 study the influence of some $p$-subgroups of $G$ satisfying the $\Pi $-property on the structure of $G$, and generalize some known results.},
author = {Qiu, Zhengtian, Liu, Jianjun, Chen, Guiyun},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite group; $p$-supersoluble group; $p$-nilpotent group; $\Pi $-property},
language = {eng},
number = {4},
pages = {1349-1358},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $\Pi $-property of some maximal subgroups of Sylow subgroups of finite groups},
url = {http://eudml.org/doc/299576},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Qiu, Zhengtian
AU - Liu, Jianjun
AU - Chen, Guiyun
TI - On $\Pi $-property of some maximal subgroups of Sylow subgroups of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1349
EP - 1358
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 study the influence of some $p$-subgroups of $G$ satisfying the $\Pi $-property on the structure of $G$, and generalize some known results.
LA - eng
KW - finite group; $p$-supersoluble group; $p$-nilpotent group; $\Pi $-property
UR - http://eudml.org/doc/299576
ER -

References

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