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The Characterisation of the Suzuki Groups by Their Sylow 2-Subgroups.

Michael J. Collins (1971)

Mathematische Zeitschrift

The Core-Free Groups of Sylow-2-type M24.

Hedwig Sandlöbes, Ulrich Schoenwaelder (1979)

Mathematische Zeitschrift

The $D_{π}$ -property of linear and unitary groups.

Revin, D.O. (2008)

Sibirskij Matematicheskij Zhurnal

The determination of abelian Hall subgroups by a conjugacy class structure.

Wolfgang Kimmerle, Robert Sandling (1992)

Publicacions Matemàtiques

The object of this article is to show that a Jordan-Hölder class structure of a finite group determines abelian Hall subgroups of the group up to isomorphism. The proof uses this classification of the finite simple groups.

The Fitting class generated by the $π$ -perfect groups

Brison, Owen J. (1990)

Portugaliae mathematica

The influence of weakly-supplemented subgroups on the structure of finite groups

Qingjun Kong, Qingfeng Liu (2014)

Czechoslovak Mathematical Journal

A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G = H K$ . In the paper it is proved that a finite group $G$ is $p$ -nilpotent provided $p$ is the smallest prime number dividing the order of $G$ and every minimal subgroup of $P \cap G^{'}$ is weakly-supplemented in $N_{G} (P),$ where $P$ is a Sylow $p$ -subgroup of $G$ . As applications, some interesting results with weakly-supplemented minimal subgroups of $P \cap G^{'}$ are obtained.

The other $P (G, V)$ -theorem

U. Meierfrankenfeld, B. Stellmacher (2006)

Rendiconti del Seminario Matematico della Università di Padova

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.

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

Michel Broué, Gunter Malle (1992)

Mathematische Annalen

Théorèmes sur les groupes de substitutions

Sylow (1872)