Shengmin Zhang

collaborators

7 papers

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.GR2024

A new characterization of $E_{8} (p)$ via its vanishing elements

Shengmin Zhang

Let $G$ be a finite group, and $g \in G$ . Then $g$ is said to be a vanishing element of $G$ , if there exists an irreducible character $χ$ of $G$ such that $χ (g) = 0$ . Denote by ${\rm…

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…

math.GR2023

On the $I C S P C$ -property of finite subgroups

Shengmin Zhang

Let $G$ be a finite group and $H$ be a subgroup of $G$ . Then $H$ is said to be a $p$ - $C A P$ -subgroup of $G$ , if $H$ covers or avoids any $p d$ -chief factor of $G$ . Furthermore, $H$ i…

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

A new characterization of E8​(p) via its vanishing elements

On the finite solvable PNC-groups

On the ICSPC-property of finite subgroups

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

A new characterization of $E_{8} (p)$ via its vanishing elements

On the finite solvable $P N C$ -groups

On the $I C S P C$ -property of finite subgroups