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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...

Nel presente lavoro vengono dimostrati teoremi d'esistenza di $p$ -complementi normali nei gruppi finiti.

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Displaying 181 – 200 of 249

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

The $p^{*} p$ -injectors of a finite group

The pi-separability of Certain Factorizable Groups.

The superfocal subgroup

Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis.

Théorèmes sur les groupes de substitutions

Über den grössten p-Normalteiler einer endlichen Gruppe.

Über einige Eigenschaften der Zentralreihe der p-Sylowgruppe der symmetrischen Gruppe vom Grade pm

Una generalización del teorema de Schur-Zassenhaus.

Une caractérisation des groupes $π$ -résolubles

Untergruppenverbände endlicher Gruppen mit elementarabelschen Hallschen Normalteilern.

Verschränkte Homomorphismen endlicher Gruppen.

Weights for the Steinberg triality groups 3D4(q).

$Π$ -normally embedded subgroups of finite soluble groups

$π$ -подгруппы Силова классических групп

$τ$ -primitive subgroups of finite groups.

Автоморфизмы, факторизации и теоремы типа Силова

Большие нильпотентные подгруппы конечных простых групп

Влияние $π$ -свойств подгрупп на свойства конечной группы

Квазинильпотентные группы

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