Xiaoyu Chen

activity

20082020

most citedConvex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B

30 citations · 69 across the 20 of their papers we have counts for

collaborators

20 papers

math.RT2020

Irreducible Modules of Reductive Groups with Borel-stable Line

Xiaoyu Chen

Let $p$ be a prime number and $k = F ˉ_{p}$ , the algebraic closure of the finite field $F_{p}$ of $p$ elements. Let $G$ be a connected reductive group def…

math.RT2019

Abstract induced modules for reductive algebraic groups with Frobenius maps

Xiaoyu Chen, Junbin Dong

Let $G$ be a connected reductive algebraic group defined over a finite field $F_{q}$ of $q$ elements, and $B$ be a Borel subgroup of $G$ defined over $\mat…

math.RT2019

The Decomposition of Permutation Module for Infinite Chevalley Groups

Xiaoyu Chen, Junbin Dong

Let $G$ be a connected reductive group defined over $F_{q}$ , the finite field with $q$ elements. Let $B$ be an Borel subgroup defined over $F_{q}$ . In thi…

math.RT2017

The Permutation Module on Flag Varieties in Cross Characteristic

Xiaoyu Chen, Junbin Dong

Let $G$ be a connected reductive group over $F ˉ_{q}$ , the algebraically closure of $F_{q}$ (the finite field with $q = p^{e}$ elements), with the standard Frob…

math.RT2017★ 1 cited

Some Non Quasi-finite irreducible Modules of Semisimple Groups with Frobenius Maps

Xiaoyu Chen

This paper is the continuation of \cite{CXY}. Let $G$ be a simply connected semisimple algebraic group over $k = F ˉ_{q}$ , the algebraically closure of $\mathbb{…

math.RT2017★ 6 cited

On the principal series representations of semisimple groups with Frobenius maps

Xiaoyu Chen

Let $G$ be a simply connected semisimple algebraic group over $k = F ˉ_{q}$ , the algebraically closure of $F_{q}$ (the finite field with $q = p^{e}$ elements)…

math.QA2016★ 1 cited

Convex PBW-type Lyndon Bases and Restricted Two-Parameter Quantum Group of Type $F_{4}$

Xiaoyu Chen, Naihong Hu, Xiuling Wang

We determine convex PBW-type Lyndon bases for two-parameter quantum groups $U_{r, s} (F_{4})$ with detailed commutation relations. We construct a finite-dimensional Hopf algebra $\math…

math.GR2015

On a problem from the Kourovka Notebook

Xiaoyu Chen

In this manuscript, a solution to Problem 18.91(b) in the Kourovka Notebook is given by proving the following theorem. Let $P$ be a Sylow $p$ -subgroup of a group $G$ with $|P| = p^…

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 the converse of Hall's theorem

Xiaoyu Chen

In this paper, we mainly investigate the converse of a well-known theorem proved by P. Hall, and present detailed characterizations under the various assumptions of the existence o…

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

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★ 6 cited

On weakly S-embedded subgroups and weakly $τ$ -embedded subgroups

Xiaoyu Chen, Wenbin Guo

Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be weakly S-embedded in $G$ if there exists $K ⊴ G$ such that $H K$ is S-quasinormal in $G$ and $H \cap K \leq H_{se G}$ …

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 $…

math.GR2013★ 6 cited

On partial $Π$ -property of subgroups of finite groups

Xiaoyu Chen, Wenbin Guo

Let $H$ be a subgroup of a finite group $G$ . We say that $H$ satisfies partial $Π$ -property in $G$ if there exists a chief series $Γ_{G} : 1 = G_{0} < G_{1} < \dots < G_{n} = G$ of $G$ such th…

math.QA2008★ 30 cited

Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B

Naihong Hu, Xiuling Wang

We construct convex PBW-type Lyndon bases for two-parameter quantum groups U_{r,s}({so}_{2n+1}) with detailed commutation relations. It turns out that under a certain condition, th…

Irreducible Modules of Reductive Groups with Borel-stable Line

Abstract induced modules for reductive algebraic groups with Frobenius maps

The Decomposition of Permutation Module for Infinite Chevalley Groups

The Permutation Module on Flag Varieties in Cross Characteristic

Some Non Quasi-finite irreducible Modules of Semisimple Groups with Frobenius Maps

On the principal series representations of semisimple groups with Frobenius maps

Convex PBW-type Lyndon Bases and Restricted Two-Parameter Quantum Group of Type F4​

On a problem from the Kourovka Notebook

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

On the converse of Hall's theorem

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

On HC-subgroups of a finite group

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

On weakly S-embedded subgroups and weakly τ-embedded subgroups

Finite groups in which SS-permutability is a transitive relation

On partial Π-property of subgroups of finite groups

Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B

Convex PBW-type Lyndon Bases and Restricted Two-Parameter Quantum Group of Type $F_{4}$

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

On weakly S-embedded subgroups and weakly $τ$ -embedded subgroups

On partial $Π$ -property of subgroups of finite groups