HUN-REN Alfréd Rényi Institute of Mathematics

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19942026

most citedBrownian distance covariance

857 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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32 papers · 1 filter

math.GR2024

Involutions in finite simple groups as products of conjugates

Daniele Dona, Martin W. Liebeck, Kamilla Rekvényi

Let $G$ be a finite non-abelian simple group, $C$ a non-identity conjugacy class of $G$ , and $Γ_{C}$ the Cayley graph of $G$ based on $C \cup C^{- 1}$ . Our main result shows that in a…

math.GR2024★ 3 cited

Growth of products of subsets in finite simple groups

Daniele Dona, Attila Maróti, László Pyber

We prove that the product of a subset and a normal subset inside any finite simple non-abelian group $G$ grows rapidly. More precisely, if $A$ and $B$ are two subsets with $B$ norm…

math.GR2023

New dimensional estimates for subvarieties of linear algebraic groups

Jitendra Bajpai, Daniele Dona, Harald Andrés Helfgott

For every connected, almost simple linear algebraic group $G \leq GL_{n}$ over a large enough field $K$ , every subvariety $V \subseteq G$ , and every finite generating set $A\…

math.GR2023★ 1 cited

On finite $d$ -maximal groups

Andrea Lucchini, Luca Sabatini, Mima Stanojkovski

Let $d$ be a positive integer. A finite group is called $d$ -maximal if it can be generated by precisely $d$ elements, while its proper subgroups have smaller generating sets. For $…

math.GR2023★ 1 cited

Finite Class 2 Nilpotent and Heisenberg Groups

Dávid R. Szabó

We present a structural description of finite nilpotent groups of class at most $2$ using a specified number of subdirect and central products of $2$ -generated such groups. As a co…

math.GR2022★ 1 cited

Products of subgroups, subnormality, and relative orders of elements

Luca Sabatini

Let $G$ be a group. We give an explicit description of the set of elements $x \in G$ such that $x^{∣ G : H ∣} \in H$ for every subgroup of finite index $H ⩽ G$ . This is related…

math.GR2022★ 3 cited

Conjugacy classes of $π$ -elements and nilpotent/abelian Hall $π$ -subgroups

N. N. Hung, A. Maróti, J. Martínez

Let $G$ be a finite group and $π$ be a set of primes. We study finite groups with a large number of conjugacy classes of $π$ -elements. In particular, we obtain precise lower bounds…

math.GR2022★ 1 cited

On groups with large verbal quotients

Francesca Lisi, Luca Sabatini

Let $w = w (x_{1}, ..., x_{n})$ be a word, i.e. an element of the free group $F = ⟨ x_{1}, ..., x_{n} ⟩$ . The verbal subgroup $w (G)$ of a group $G$ is the subgroup generated by the se…

math.GR2021

Growth in linear groups

Sean Eberhard, Brendan Murphy, László Pyber +1

We prove a conjecture of Helfgott on the structure of sets of bounded tripling in bounded rank, which states the following. Let $A$ be a finite symmetric subset of $\mathrm{GL}_n(\…

math.GR2021★ 2 cited

The growth of abelian sections

Luca Sabatini

Given an abstract group $G$ , we study the function $a b_{n} (G) := sup_{∣ G : H ∣ \leq n} ∣ H / [H, H] ∣$ . If $G$ has no abelian composition factors, then $a b_{n} (G)$ is bounded by a polynomial:…

math.GR2020★ 11 cited

Bounding the number of classes of a finite group in terms of a prime

Attila Maróti, Iulian I. Simion

Héthelyi and Külshammer showed that the number of conjugacy classes $k (G)$ of any solvable finite group $G$ whose order is divisible by the square of a prime $p$ is at least $(49p+…

math.GR2019★ 6 cited

On the generalized Fitting height and insoluble length of finite groups

Robert M. Guralnick, Gareth Tracey

We prove two conjectures of E. Khukhro and P. Shumyatsky concerning the Fitting height and insoluble length of finite groups. As a by-product of our methods, we also prove a genera…

math.GR2019★ 7 cited

$F$ -inverse monoids as algebraic structures in enriched signature

K. Auinger, G. Kudryavtseva, M. B. Szendrei

Every $F$ -inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $σ$ -class. In this enriched signature, the class of all $F$ -…

math.GR2019★ 3 cited

A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank

N. Gill, L. Pyber, E. Szabó

We prove that if $G$ is a finite simple group of Lie type and $S_{1}, \dots, S_{k}$ are subsets of $G$ satisfying $\prod_{i = 1}^{k} ∣ S_{i} ∣ \geq ∣ G ∣^{c}$ for some $c$ depending only on the rank o…

math.GR2018★ 4 cited

An improved diameter bound for finite simple groups of Lie type

Zoltán Halasi, Attila Maróti, László Pyber +1

For a finite group $G$ , let $diam (G)$ denote the maximum diameter of a connected Cayley graph of $G$ . A well-known conjecture of Babai states that $diam (G)$ is bo…

math.GR2017★ 2 cited

Set-Direct Factorizations of Groups

Dan Levy, Attila Maróti

We consider factorizations $G = X Y$ where $G$ is a general group, $X$ and $Y$ are normal subsets of $G$ and any $g \in G$ has a unique representation $g = x y$ with $x \in X$ and $y \in Y$ …

math.GR2017★ 32 cited

The Noether numbers and the Davenport constants of the groups of order less than 32

Kálmán Cziszter, Mátyás Domokos, István Szöllősi

The computation of the Noether numbers of all groups of order less than thirty-two is completed. It turns out that for these groups in non-modular characteristic the Noether number…

math.GR2016★ 26 cited

A proof of Pyber's base size conjecture

Hülya Duyan, Zoltán Halasi, Attila Maróti

Building on earlier papers of several authors, we establish that there exists a universal constant $c > 0$ such that the minimal base size $b (G)$ of a primitive permutation group $…

math.GR2015★ 1 cited

Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent

Martino Garonzi, Dan Levy, Attila Maróti +1

We consider factorizations of a finite group $G$ into conjugate subgroups, $G = A^{x_{1}} \dots A^{x_{k}}$ for $A \leq G$ and $x_{1}, \dots, x_{k} \in G$ , where $A$ is nilpotent or sol…

math.GR2014★ 1 cited

On the number of $p^{'}$ -degree characters in a finite group

Gunter Malle, Attila Maróti

Let $p$ be a prime divisor of the order of a finite group $G$ . Then $G$ has at least $2 p - 1$ complex irreducible characters of degrees prime to $p$ . In case $p$ is a prime w…

math.GR2014★ 1 cited

A lower bound for the number of conjugacy classes of a finite group

Attila Maróti

Every finite group whose order is divisible by a prime $p$ has at least $2 p - 1$ conjugacy classes.

math.GR2014

On a conjecture of Gluck

James P. Cossey, Zoltán Halasi, Attila Maróti +1

Let $F (G)$ and $b (G)$ respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group $G$ . A well-known conjecture of D. Gluck…

math.GR2013★ 11 cited

The minimal base size for a p-solvable linear group

Zoltán Halasi, Attila Maróti

Let $V$ be a finite vector space over a finite field of order $q$ and of characteristic $p$ . Let $G \leq G L (V)$ be a $p$ -solvable completely reducible linear group. Then there exist…

math.GR2012★ 18 cited

Every coprime linear group admits a base of size two

Zoltán Halasi, Károly Podoski

Let G be a linear group acting on the finite vector space V and assume that (|G|,|V|)=1. In this paper we prove that G has a base size at most two and this estimate is sharp. This…