Zhencai Shen

collaborators

5 papers

math.GR2024

Some results on the norm of finite groups

Mark L. Lewis, Zhencai Shen, Quanfu Yan

Let $G$ be a finite group and $N_{Ω} (G)$ be the intersection of the normalizers of all subgroups belonging to the set $Ω (G),$ where $Ω (G)$ is a set of all subgroups of $G$ which have…

math.GR2024

New characterizations for supersolvability of fusion system and $p$ -nilpotency of finite groups

Shengmin Zhang, Zhencai Shen

Let $p$ be a prime, $S$ be a $p$ -group and $F$ be a saturated fusion system over $S$ . Then $F$ is said to be supersolvable, if there exists a series of $S$ , nam…

math.GR2024

The influence of weakly $S Φ$ -supplemented subgroups on fusion systems of finite groups

Shengmin Zhang, Zhencai Shen

Let $G$ be a finite group and $H$ be a subgroup of $G$ . Then $H$ is called a weakly $S Φ$ -supplemented subgroup of $G$ , if there exists a subgroup $T$ of $G$ such that $G = H T$ and $…

math.GR2024

On generalized covering and avoidance properties of finite groups and saturated fusion systems

Shengmin Zhang, Zhencai Shen

A subgroup $A$ of a finite group $G$ is said to be a $C A P$ -subgroup of $G$ , if for any chief factor $H / K$ of $G$ , either $A H = A K$ or $A \cap H = A \cap K$ . Let $p$ be a prime, $S$ …

math.GR2023

On the finite solvable $P N C$ -groups

Shengmin Zhang, Zhencai Shen

A subgroup $H$ of a finite group $G$ is said to be an NC-subgroup of $G$ , if $H^{G} N_{G} (H) = G$ , where $H^{G}$ denotes the normal closure of $H$ in $G$ . A finite group $G$ is called a…

Some results on the norm of finite groups

New characterizations for supersolvability of fusion system and p-nilpotency of finite groups

The influence of weakly SΦ-supplemented subgroups on fusion systems of finite groups

On generalized covering and avoidance properties of finite groups and saturated fusion systems

On the finite solvable PNC-groups

New characterizations for supersolvability of fusion system and $p$ -nilpotency of finite groups

The influence of weakly $S Φ$ -supplemented subgroups on fusion systems of finite groups

On the finite solvable $P N C$ -groups