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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...

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Currently displaying 1 – 10 of 10

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

Some new Hilbert's type inequalities.

Inverses of new Hilbert-Pachpatte-type inequalities.

On Opial-type integral inequalities.

On a discrete Opial-type inequality.

Width-integrals and affine surface area of convex bodies.

On generalizations of L. Yang's inequality.

The Aleksandrov-Fenchel type inequalities for volume differences.

On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.

Some new Brunn-Minkowski-type inequalities in convex bodies.