Attila Mar'oti

activity

20132021

most citedA proof of Pyber's base size conjecture

26 citations · 59 across the 9 of their papers we have counts for

collaborators

16 papers

math.RT2021★ 2 cited

On almost $p$ -rational characters of $p^{'}$ -degree

Nguyen Ngoc Hung, Gunter Malle, Attila Maróti

Let $p$ be a prime and $G$ a finite group. A complex character of $G$ is called almost $p$ -rational if its values belong to a cyclotomic field $Q (e^{2 π i / n})$ for some $n\i…

math.GR2020

On the maximal number of elements pairwise generating the symmetric group of even degree

Francesco Fumagalli, Martino Garonzi, Attila Maróti

Let $G$ be the symmetric group of degree $n$ . Let $ω (G)$ be the maximal size of a subset $S$ of $G$ such that $⟨ x, y ⟩ = G$ whenever $x, y \in S$ and $x \neq = y$ and let…

math.GR2020

Alternating groups as products of four conjugacy classes

Martino Garonzi, Attila Maróti

Let $G$ be the alternating group $\mbox{Alt}(n)$ on $n$ letters. We prove that for any $ε > 0$ there exists $N = N (ε) \in N$ such that whenever $n \geq…

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.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.GR2018

Finite simple groups with short Galois orbits on conjugacy classes

Victor Bovdi, Thomas Breuer, Attila Maróti

All finite simple groups are determined with the property that every Galois orbit on conjugacy classes has size at most 4. From this we list all finite simple groups $G$ for which…

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

Finite groups with large Noether number are almost cyclic

Pál Hegedűs, Attila Maróti, László Pyber

Noether, Fleischmann and Fogarty proved that if the characteristic of the underlying field does not divide the order $∣ G ∣$ of a finite group $G$ , then the polynomial invariants of…

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.GR2016

Normalizers of Primitive Permutation Groups

Robert M. Guralnick, Attila Maróti, László Pyber

Let $G$ be a transitive normal subgroup of a permutation group $A$ of finite degree $n$ . The factor group $A / G$ can be considered as a certain Galois group and one would like to bo…

math.GR2015

Primitive permutation groups as products of point stabilizers

Martino Garonzi, Dan Levy, Attila Maróti +1

We prove that there exists a universal constant $c$ such that any finite primitive permutation group of degree $n$ with a non-trivial point stabilizer is a product of no more than…

math.GR2015

Finite groups have more conjugacy classes

Barbara Baumeister, Attila Maróti, Hung P. Tong-Viet

We prove that for every $ε > 0$ there exists a $δ > 0$ so that every group of order $n \geq 3$ has at least $δ lo g_{2} n / (lo g_{2} lo g_{2} n)^{3 + ε}$ conjugacy classes. This sharpe…

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.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…

On almost p-rational characters of p′-degree