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$D_{p} (3)$ (p ≥ 5) can be characterized by its order components

Huaguo Shi; Zhangjia Han; Guiyun Chen — 2012

Colloquium Mathematicae

Let G be a finite group, and $M = D_{p} (3)$ (p ≥ 3). It is proved that G ≅ M if G and M have the same order components.

The $p$ -nilpotency of finite groups with some weakly pronormal subgroups

Jianjun Liu; Jian Chang; Guiyun Chen — 2020

Czechoslovak Mathematical Journal

For a finite group $G$ and a fixed Sylow $p$ -subgroup $P$ of $G$ , Ballester-Bolinches and Guo proved in 2000 that $G$ is $p$ -nilpotent if every element of $P \cap G^{'}$ with order $p$ lies in the center of $N_{G} (P)$ and when $p = 2$ , either every element of $P \cap G^{'}$ with order $4$ lies in the center of $N_{G} (P)$ or $P$ is quaternion-free and $N_{G} (P)$ is $2$ -nilpotent. Asaad introduced weakly pronormal subgroup of $G$ in 2014 and proved that $G$ is $p$ -nilpotent if every element of $P$ with order $p$ is weakly pronormal in $G$ and when $p = 2$ , every element of $P$ with order $4$ is also...

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

Zhengtian Qiu; Guiyun Chen; Jianjun Liu — 2024

Czechoslovak Mathematical Journal

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 $G$ , $| G / K : N_{G / K} (H K / K \cap L / K) |$ is a $π (H K / K \cap L / K)$ -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 $Π$ -property.

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Currently displaying 1 – 6 of 6

$D_{p} (3)$ (p ≥ 5) can be characterized by its order components

The $p$ -nilpotency of finite groups with some weakly pronormal subgroups

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

A characterization of alternating groups by the set of orders of maximal Abelian subgroups.

A characterization theorem for sporadic simple groups.

Recognition of the finite simple groups $F_{4} (2^{m})$ by the spectrum.

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Currently displaying 1 – 6 of 6

D p ( 3 ) (p ≥ 5) can be characterized by its order components

The p -nilpotency of finite groups with some weakly pronormal subgroups

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

A characterization of alternating groups by the set of orders of maximal Abelian subgroups.

A characterization theorem for sporadic simple groups.

Recognition of the finite simple groups F 4 ( 2 m ) by the spectrum.

$D_{p} (3)$ (p ≥ 5) can be characterized by its order components

The $p$ -nilpotency of finite groups with some weakly pronormal subgroups

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

Recognition of the finite simple groups $F_{4} (2^{m})$ by the spectrum.