Wenbin Guo

activity

20122022

π

F

-norm and the

H

F

-norm of a finite group

13 citations · 67 across the 27 of their papers we have counts for

collaborators

27 papers

math.GR2022★ 1 cited

On embedding theorems for $X$ -subgroups

Wenbin Guo, Danila O. Revin, Andrey V. Vasil'ev

Let $X$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1…

math.GR2021★ 2 cited

On Cayley representations of central Cayley graphs over almost simple groups

Jin Guo, Wenbin Guo, Grigory Ryabov +1

A Cayley graph over a group $G$ is said to be central if its connection set is a normal subset of $G$ . We prove that every central Cayley graph over a simple group $G$ has at most…

math.GR2021

When is the search of relatively maximal subgroups reduced to quotients?

Wenbin Guo, Danila O. Revin

Let $X$ be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Denote by $k_{X} (G)$ the number of conjuga…

math.GR2020

On a generalisation of finite $T$ -groups

Chi Zhang, Wenbin Guo

Let $σ = {σ_{i} ∣ i \in I}$ is some partition of all primes $P$ and $G$ a finite group. A subgroup $H$ of $G$ is said to be $σ$ -subnormal in $G$ if there exists a subgroup cha…

math.GR2018★ 3 cited

Spectra of Cayley graphs

Wenbin Guo, Daria V. Lytkina, Victor D. Mazurov +1

Let $G$ be a group and $S \subseteq G$ its subset such that $S = S^{- 1}$ , where $S^{- 1} = {s^{- 1} ∣ s \in S}$ . Then {\it the Cayley graph $Cay (G, S)$ } is an undirected graph $Γ$ …

math.GR2018★ 6 cited

The reduction theorem for relatively maximal subgroups

Wenbin Guo, Danila O. Revin, Evgeny P. Vdovin

Let $X$ be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if $A$ is a normal subgroup of a finite group $G$ …

math.GR2018

Finite groups with Frobenius normalizer condition for non-normal primary subgroups

Zhang Chi, Wenbin Guo

A finite group $P$ is said to be \emph{primary} if $∣ P ∣ = p^{a}$ for some prime $p$ . We say a primary subgroup $P$ of a finite group $G$ satisfies the \emph{Frobenius normalizer cond…

math.GR2018

On an open problem of Skiba

Zhenfeng Wu, Chi Zhang, Wenbin Guo

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set $P$ of all primes, that is, $P = ⋃_{i \in I} σ_{i}$ and $σ_{i} \cap σ_{j} = \emptyset$ for all $i \neq = j$ . Let…

math.GR2017★ 1 cited

Number of Sylow subgroups in finite groups

Wenbin Guo, Evgeny Vdovin

Denote by $ν_{p} (G)$ the number of Sylow $p$ -subgroups of $G$ . It is not difficult to see that $ν_{p} (H) \leq ν_{p} (G)$ for $H \leq G$ , however $ν_{p} (H)$ does not divide $ν_{p} (G)$ in general.…

math.GR2017★ 9 cited

Classification and properties of the $π$ -submaximal subgroups in minimal nonsolvable groups

Wenbin Guo, Danila Revin

Let $π$ be a set of primes. According to H. Wielandt, a subgroup $H$ of a finite group $X$ is called a $π$ -submaximal subgroup if there is a monomorphism $ϕ : X \to Y$ into a…

math.GR2017

On $H_{σ}$ -permutably embedded and $H_{σ}$ -subnormaly embedded subgroups of finite groups

Wenbin Guo, Chi Zhang, Alexander N. Skiba +1

Let $G$ be a finite group. Let $σ = {σ_{i} ∣ i \in I}$ be a partition of the set of all primes $P$ and $n$ an integer. We write $σ (n) = {σ_{i} ∣ σ_{i} \cap π (n) \neq = \emptyset}$ …

math.GR2016

On $σ$ -semipermutable subgroups of finite groups

Wenbin Guo, Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ , $G$ a finite group and $σ (G) = {σ_{i} ∣ σ_{i} \cap π (G) \neq = \emptyset}$ . A set $H$ of subgrou…

math.GR2016★ 7 cited

Finite groups whose $n$ -maximal subgroups are $σ$ -subnormal

Wenbin Guo, Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ . A set $H$ of subgroups of $G$ is said to be a \emph{complete Hall $σ$ -set} of $G$ if every m…

math.GR2016★ 4 cited

On $Π$ -permutable subgroups of finite groups

Wenbin Guo, A. N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ and $Π$ a non-empty subset of the set $σ$ . A set $H$ of subgroups of a finite group $G$ is sa…

math.GR2015

On supersolubility of finite groups admitting a Frobenius group of automorphisms with fixed-point-free kernel

Xingzheng Tang, Xiaoyu Chen, Wenbin Guo

Assume that a finite group $G$ admits a Frobenius group of automorphisms $F H$ with kernel $F$ and complement $H$ such that $C_{G} (F) = 1$ . In this paper, we investigate this situatio…

math.GR2015

On finite groups with some primary subgroups satisfying partial $S$ - $Π$ -property

Xiaoyu Chen, Yuemei Mao, Wenbin Guo

A $p$ -subgroup $H$ of a finite group $G$ is said to satisfy partial $S$ - $Π$ -property in $G$ if $G$ has a chief series $Γ_{G} : 1 = G_{0} < G_{1} < \dots < G_{n} = G$ such that for every $G$ -…

math.GR2014

On HC-subgroups of a finite group

Lijun Huo, Xiaoyu Chen, Wenbin Guo

A subgroup $H$ of a finite group $G$ is said to be an $H C$ -subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $G = H T$ and $H^{g} \cap N_{T} (H) \leq H$ for a…

math.GR2014

Finite groups with generalized Ore supplement conditions for primary subgroups

Wenbin Guo, Alexander N. Skiba

We consider some applications of the theory of generalized Ore supplement conditions in the study of finite groups.

math.GR2014★ 9 cited

Confirmation for Wielandt's conjecture

Wenbin Guo, Danila Revin, Evgeny Vdovin

Let $π$ be a set of primes. By H.Wielandt definition, {\it Sylow $π$ -theorem} holds for a finite group $G$ if all maximal $π$ -subgroups of $G$ are conjugate. In the paper, the foll…

math.GR2014

On weakly $F_{s}$ -quasinormal subgroups of finite groups

Yuemei Mao, Xiaoyu Chen, Wenbin Guo

Let $F$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $F_{s}$ -quasinormal in $G$ if $G$ has an $S$ -quasinormal subgroup $T…

math.GR2014

The influence of $F_{s}$ -quasinormality of subgroups on the structure of finite groups

Xiaolong Yu, Xiaoyu Chen, Wenbin Guo

Let $F$ be a class of finite groups. A subgroup $H$ of a finite group $G$ is said to be $F_{s}$ -quasinormal in $G$ if there exists a normal subgroup $T$ o…

math.GR2013★ 13 cited

On the $π$ $F$ -norm and the $H$ - $F$ -norm of a finite group

Xiaoyu Chen, Wenbin Guo

Let $H$ be a Fitting class and $F$ a formation. We call a subgroup $N_{H, F} (G)$ of a finite group $G$ the $H$ -$\mat…

math.GR2013★ 1 cited

On $Π$ -supplemented subgroups of a finite group

Xiaoyu Chen, Wenbin Guo

A subgroup $H$ of a finite group $G$ is said to satisfy $Π$ -property in $G$ if for every chief factor $L / K$ of $G$ , $∣ G / K : N_{G / K} (H K / K \cap L / K) ∣$ is a $π (H K / K \cap L / K)$ -number. A s…

math.GR2013★ 5 cited

Finite groups in which SS-permutability is a transitive relation

Xiaoyu Chen, Wenbin Guo

A subgroup $H$ of a finite group $G$ is said to be SS-permutable in $G$ if $H$ has a supplement $K$ in $G$ such that $H$ permutes with every Sylow subgroup of $K$ . A finite group $…

On embedding theorems for X-subgroups

On Cayley representations of central Cayley graphs over almost simple groups

When is the search of relatively maximal subgroups reduced to quotients?

On a generalisation of finite T-groups

Spectra of Cayley graphs

The reduction theorem for relatively maximal subgroups

Finite groups with Frobenius normalizer condition for non-normal primary subgroups

On an open problem of Skiba

Number of Sylow subgroups in finite groups

Classification and properties of the π-submaximal subgroups in minimal nonsolvable groups

On Hσ​-permutably embedded and Hσ​-subnormaly embedded subgroups of finite groups

On σ-semipermutable subgroups of finite groups

Finite groups whose n-maximal subgroups are σ-subnormal

On Π-permutable subgroups of finite groups

On supersolubility of finite groups admitting a Frobenius group of automorphisms with fixed-point-free kernel

On finite groups with some primary subgroups satisfying partial S-Π-property

On HC-subgroups of a finite group

Finite groups with generalized Ore supplement conditions for primary subgroups

Confirmation for Wielandt's conjecture

On weakly Fs​-quasinormal subgroups of finite groups

The influence of Fs​-quasinormality of subgroups on the structure of finite groups

On the πF-norm and the H-F-norm of a finite group

On Π-supplemented subgroups of a finite group

Finite groups in which SS-permutability is a transitive relation

On embedding theorems for $X$ -subgroups

On a generalisation of finite $T$ -groups

Classification and properties of the $π$ -submaximal subgroups in minimal nonsolvable groups

On $H_{σ}$ -permutably embedded and $H_{σ}$ -subnormaly embedded subgroups of finite groups

On $σ$ -semipermutable subgroups of finite groups

Finite groups whose $n$ -maximal subgroups are $σ$ -subnormal

On $Π$ -permutable subgroups of finite groups

On finite groups with some primary subgroups satisfying partial $S$ - $Π$ -property

On weakly $F_{s}$ -quasinormal subgroups of finite groups

The influence of $F_{s}$ -quasinormality of subgroups on the structure of finite groups

On the $π$ $F$ -norm and the $H$ - $F$ -norm of a finite group

On $Π$ -supplemented subgroups of a finite group