Chi Zhang

activity

20152023

most citedDiagonalizable Higher Degree Forms and Symmetric Tensors

15 citations · 28 across the 17 of their papers we have counts for

collaborators

18 papers

math.GR2023

New characterizations of a normal subgroup to be hypercyclically embedded

Chenchen Cao, Zhenfeng Wu, Chi Zhang

A normal subgroup $E$ of a group $G$ is said to be hypercyclically embedded in $G$ if either $E = 1$ or $E \neq = 1$ and every chief factor of $G$ below $E$ is cyclic. In this article,…

math.RA2022

Harrison center and products of sums of powers

Hua-Lin Huang, Lili Liao, Huajun Lu +1

This paper is mainly concerned with identities like \[ (x_1^d + x_2^d + \cdots + x_r^d) (y_1^d + y_2^d + \cdots y_n^d) = z_1^d + z_2^d + \cdots + z_n^d \] where $d > 2,$ $x=(x_1, x_2…

math.RA2021

Centers of Multilinear Forms and Applications

Hua-Lin Huang, Huajun Lu, Yu Ye +1

In this paper we study the center algebras of multilinear forms. It is shown that the center of a nondegenerate multilinear form is a finite dimensional commutative algebra and can…

math.NT2021

A Solution of Sierpinski Problem Based m

Chi Zhang

In 1960, W. Sierpinski proved that there are infinitely many positive odd numbers $k$ , such that for any positive integer $n$ , $k \times 2^{n} + 1$ is a composite number. Such numbers ar…

math.GR2021

On finite groups factorized by $σ$ -nilpotent subgroups

Zhenfeng Wu, Chi Zhang

Let $G$ be a finite group and $σ = {σ_{i} ∣ i \in I}$ be a partition of the set of all primes $P$ , that is, $P = ⋃_{i \in I} σ_{i}$ and $σ_{i} \cap σ_{j} = \emptyset$ …

math.RA2020★ 9 cited

On Centers and Direct Sum Decompositions of Higher Degree Forms

Hua-Lin Huang, Huajun Lu, Yu Ye +1

Higher degree forms are homogeneous polynomials of degree $d > 2,$ or equivalently symmetric $d$ -linear spaces. This paper is mainly concerned about the algebraic structure of the…

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.RA2020★ 15 cited

Diagonalizable Higher Degree Forms and Symmetric Tensors

Hua-Lin Huang, Huajun Lu, Yu Ye +1

We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors i…

math.GR2020

Extension of elementary $p$ -groups and its application in classification of groups of prime exponent

Zheyan Wan, Yu Ye, Chi Zhang

Let $p$ be a prime number and $Z_{p} = Z / p Z$ . We study finite groups with abelian derived subgroup and exponent $p$ in terms of group extension data and thei…

math.AG2019

On the fundamental group of open Richardson varieties

Changzheng Li, Frank Sottile, Chi Zhang

We compute the fundamental group of an open Richardson variety in the manifold of complete flags that corresponds to a partial flag manifold. Rietsch showed that these log Calabi-Y…

math.AG2019★ 1 cited

On Frobenius-Perron Dimension

Changzheng Li, Ryan M. Shifler, Mingzhi Yang +1

We propose a notion of Frobenius-Perron dimension for certain free $Z$ -modules of infinite rank and compute it for the $Z$ -modules of finite dimensional complex r…

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.GR2018

On one generalization of finite nilpotent groups

Zhang Chi, Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be a partition of the set $P$ of all primes and $G$ a finite group. A chief factor $H / K$ of $G$ is said to be $σ$ -central if the semidirect product…

math.RA2017★ 1 cited

A Generalization of the Doubling Construction for Sums of Squares Identities

Chi Zhang, Hua-Lin Huang

The doubling construction is a fast and important way to generate new solutions to the Hurwitz problem on sums of squares identities from any known ones. In this short note, we gen…

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 weakly $s i g ma$ -permutable subgroups of finite groups

Chi Zhang, Zhenfeng Wu, W. Guo

Let G be a finite group and σ = {σ_i, i \in I} be a partition of the set of all primes \mathbb{P}. A set \mathcal{H} of subgroups of G with 1 \in \mathcal{H} is said to be a comple…

math.QA2015★ 2 cited

$Z_{2}^{n}$ -graded quasialgebras and the Hurwitz problem on compositions of quadratic forms

Ya-Qing Hu, Hua-Lin Huang, Chi Zhang

We introduce a series of $Z_{2}^{n}$ -graded quasialgebras $\bbP_n(m)$ which generalizes Clifford algebras, higher octonions, and higher Cayley algebras. The constructed series of alge…

New characterizations of a normal subgroup to be hypercyclically embedded

Harrison center and products of sums of powers

Centers of Multilinear Forms and Applications

A Solution of Sierpinski Problem Based m

On finite groups factorized by σ-nilpotent subgroups

On Centers and Direct Sum Decompositions of Higher Degree Forms

On a generalisation of finite T-groups

Diagonalizable Higher Degree Forms and Symmetric Tensors

Extension of elementary p-groups and its application in classification of groups of prime exponent

On the fundamental group of open Richardson varieties

On Frobenius-Perron Dimension

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

On an open problem of Skiba

On one generalization of finite nilpotent groups

A Generalization of the Doubling Construction for Sums of Squares Identities

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

On weakly sigma-permutable subgroups of finite groups

Z2n​-graded quasialgebras and the Hurwitz problem on compositions of quadratic forms

On finite groups factorized by $σ$ -nilpotent subgroups

On a generalisation of finite $T$ -groups

Extension of elementary $p$ -groups and its application in classification of groups of prime exponent

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

On weakly $s i g ma$ -permutable subgroups of finite groups

$Z_{2}^{n}$ -graded quasialgebras and the Hurwitz problem on compositions of quadratic forms