Z. Akhlaghi

activity

20172026

most citedVariations on average character degrees and solvability

1 citations · 1 across the 14 of their papers we have counts for

collaborators

20 papers

math.GR2026

Common non-zero graphs of groups with few edges

Zeinab Akhlaghi, Sesuai Yash Madanha

Let $ G $ be a finite group, and consider its common non-zero graph, which we denote by $ Γ_{nv}(G) $. In this graph, the vertices represent the non-linear irreducible characte…

math.CO2026

Finite groups with quadratic splitting fields for all Cayley graphs

Majid Arezoomand, Alireza Abdollahi, Tao Feng +1

For a graph $Γ$ , the splitting field of $Γ$ is defined as the splitting field of the characteristic polynomial of $Γ$ over rationals. The algebraic degree of $Γ$ is defined by the…

math.CO2025

Perfect codes and regular sets in vertex-transitive graphs

Alireza Abdollahi, Zeinab Akhlaghi, Majid Arezoomand

A subset $ C $ of the vertex set $ V $ of a graph $ Γ= (V,E) $ is termed an $(r, s)$ -regular set if each vertex in $ C $ is adjacent to exactly $ r $ other vertices in \(…

math.GR2024

Finite groups with coprime non-linear codegrees

Ashkan Zarezadeh, Behrooz Khosravi, Zeinab Akhlaghi

Given a finite group G with an irreducible character χ\in Irr(G), the codegree of χis defined by cod(χ) = |G :\ker χ|/χ(1). The set of non-linear irreducible character codegrees of…

math.CO2024

Regular set in Cayley sum mgraph

F. Seiedali, B. Khosravi, Z. Akhlaghi

A subset $C$ of the vertex set of a graph $Γ$ is said to be $(α, β)$ -regular if $C$ induces an $α$ -regular subgraph and every vertex outside $C$ is adjacent to exactly $β$ vertices…

math.GR2023

Some Properties of normal subgroups determined from character tables

Zeinab Akhlaghi, Maria Jose Felipe, Kelly Jean-Philippe

Gcharacter tables of a finite group G were defined before. These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of…

math.CO2023

On the subgroup regular set in Cayley graphs

Asamin Khaefi, Zeinab Akhlaghi, Behrooz Khosravi

A subset $C$ of the vertex set of a graph $Γ$ is said to be $(a, b)$ -regular if $C$ induces an $a$ -regular subgraph and every vertex outside $C$ is adjacent to exactly $b$ vertices…

math.GR2023

Characterizing some finite groups by the average order

Ashkan Zarezadeh, Behrooz Khosravi, Zeinab Akhlaghi

The average order of a finite group G is denoted by o(G). In this note, we classify groups whose average orders are less than o(S4), where S4 is the symmetric group on four element…

math.GR2023

Element orders and codegrees of characters in non-solvable groups

Z. Akhlaghi, E. Pacifici, L. Sanus

Given a finite group $G$ and an irreducible complex character $χ$ of $G$ , the codegree of $χ$ is defined as the integer $cod (χ) = ∣ G : ker χ ∣/ χ (1)$ . It was conjectured by G. Qian…

math.GR2022

Erratum to : A generalization of Taketa's Theorem on M-groups

Zeinab Akhlaghi

In the recent paper [A generalization of Taketa's theorem on M-groups, Quaestiones Mathematicae, (2022), https://doi.org/10.2989/16073606.2022.2081632], we give an upper bound 5/2…

math.GR2022★ 1 cited

Variations on average character degrees and solvability

Neda Ahanjideh, Zeinab Akhlaghi, Kamal Aziziheris

Let $G$ be a finite group, $F$ be one of the fields $Q, R$ or $C$ , and $N$ be a non-trivial normal subgroup of $G$ . Let $acd_{F}^{*} (G)$ …

math.GR2021

On the average character degree of some irreducible characters of a finite group

Zeinab Akhlaghi

Let G be a finite group and N be a non-trivial normal subgroup of G, such that the average character degree of irreducible characters in Irr(G|N) is less than or equal to 16=5. The…

math.GR2021

On the multiplicities of the character codegrees

Zeinab Akhlaghi, Mehdi Ebrahimi, Maryam Khatami

Let G be a finite group and ? be an irreducible character of G, the number cod(?) = jG : Let $G$ be a finite group and $χ$ be an irreducible character of $G$ , the number $ \co…

math.GR2021

On Huppert's Rho-Sigma Conjecture

Zeinab Akhlaghi, Silvio Dolfi, Emanuele Pacifici

For an irreducible complex character $χ$ of the finite group $G$ , let $π (χ)$ denote the set of prime divisors of the degree $χ (1)$ of $χ$ . Denote then by $ρ (G)$ the union of all th…

math.GR2020

Minimal partition-free groups

Afsane Bahri, Zeinab Akhlaghi, Behrooz Khosravi

Let G be a finite group. A collection P={H1, ..., Hr} of subgroups of G, where r > 1, is said a non-trivial partition of G if every non-identity element of G belongs to one and onl…

math.GR2020

Equivalent version of Huppert's conjecture on the codegrees

Afsane Bahri, Zeinab Akhlaghi, Behrooz Khosravi

Let G be a finite group, Irr(G) the set of all irreducible complex characters of G and X \in Irr(G). Let also cod(X) = |G : kerX|/X(1) and cod(G) = {cod(X) | X \in Irr(G)}. In this…

math.GR2019

A result on the sum of element orders of a finite group

Afsaneh Bahri, Behrooz Khosravi, Zeinab Akhlaghi

Let $G$ be a finite group and $ψ (G) = \sum_{g \in G} o (g)$ . There are some results about the relation between $ψ (G)$ and the structure of $G$ . For instance, it is proved that if $G$ …

math.GR2018

Bounding the number of vertices in the degree graph of a finite group

Zeinab Akhlaghi, Silvio Dolfi, Emanuele Pacifici +1

Let $G$ be a finite group, and let $cd (G)$ denote the set of degrees of the irreducible complex characters of $G$ . The degree graph $Δ (G)$ of $G$ is defined as the simple un…

math.GR2018

On the character degree graph of finite groups

Zeinab Akhlaghi, Carlo Casolo, Silvio Dolfi +2

Given a finite group G, let cd(G) denote the set of degrees of the irreducible complex characters of G. The character degree graph of G is defined as the simple undirected graph wh…

math.GR2017

On the character degree graph of solvable groups

Zeinab Akhlaghi, Carlo Casolo, Silvio Dolfi +2

Let $G$ be a finite solvable group, and let $Δ(G)$ denote the \emph{prime graph} built on the set of degrees of the irreducible complex characters of $G$. A fundamental resul…