Attila Maróti

On the orbital diameter of classical groups in standard actions

Attila Maróti, Kamilla Rekvényi

Abstract Let G be a primitive permutation group acting on a finite set X . The orbital diameter $$\textrm{diam}(X,G)$$ diam ( X , G ) is defined to be the supremum of the diameters of the (connected) orbital graphs of G after …

hu, gb (code pays fourni par la source)

More on Landau’s theorem and conjugacy classes

Burcu Çınarcı, Thomas Michael Keller, Attila Maróti, Iulian I. Simion

ABSTRACT In this paper we present two new results on the number of certain conjugacy classes of a finite group. For a finite group $G$, let $n(G)$ be the maximum of $k_{p}(G)$ taken over all primes $p$ where $k_{p}(G)$ denotes the number …

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On the base size and minimal degree of transitive groups

Lorenzo Guerra, Attila Maróti, Fabio Mastrogiacomo, Saveliy V. Skresanov et autres

Abstract Let 𝐺 be a permutation group, with minimal degree μ ⁢ ( G ) \mu(G) and base size b ⁢ ( G ) b(G) . We show that there exists a universal constant c > 0 c>0 such that, for infinitely …

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On the orbital diameter of classical groups in standard action

Attila Maróti, Kamilla Rekvényi

Let $G$ be a primitive permutation group acting on a finite set $X$. The orbital diameter $\mathrm{diam}(X,G)$ is defined to be the supremum of the diameters of the (connected) orbital graphs of $G$ after disregarding the directions of all edges in the …

On the orbital diameter of classical groups in standard action

Attila Maróti, Kamilla Rekvényi

Let $G$ be a primitive permutation group acting on a finite set $X$. The orbital diameter $\mathrm{diam}(X,G)$ is defined to be the supremum of the diameters of the (connected) orbital graphs of $G$ after disregarding the directions of all edges in the …

gb, hu (code pays fourni par la source)

Wreath products and the non-coprime k ( GV ) problem

Hung Ngoc Nguyen, Attila Maróti, Juan José Prieto Martínez

Abstract Let $G = X \wr H$ be the wreath product of a nontrivial finite group X with k conjugacy classes and a transitive permutation group H of degree n acting on the set of n direct factors of X n . …

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Covering the set of $p$-elements in finite groups by Sylow $p$-subgroups

Attila Maróti, Juan José Prieto Martínez, Alexander Moretó

Let $G_p$ be the set of $p$-elements of a finite group $G$. Do we need all the Sylow $p$-subgroups of $G$ to cover $G_p$? Although this question does not have an affirmative answer in general, our work indicates that the answer is …

Fixed‐point ratios, Sylow numbers, and coverings of p$p$‐elements in finite groups

Robert M. Guralnick, Attila Maróti, Juan José Prieto Martínez, Alexander Moretó et autres

Abstract Fixed‐point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime and a finite group , we use fixed‐point ratios to study the …

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Wreath products and the non-coprime $k(GV)$ problem

Hung Ngoc Nguyen, Attila Maróti, Juan Martínez Madrid

Let $G = X \wr H$ be the wreath product of a nontrivial finite group $X$ with $k$ conjugacy classes and a transitive permutation group $H$ of degree $n$ acting on the set of $n$ direct factors of $X^n$. If $H$ is …

On the Gowers trick for classical simple groups

Francesco Fumagalli, Attila Maróti

If A , B , C are subsets in a finite simple group of Lie type G at least two of which are normal with | A | | B | | C | relatively large, then we establish a stronger conclusion …

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Covering the set of p-elements in finite groups by proper subgroups

Attila Maróti, Juan José Prieto Martínez, Alexander Moretó

Let p be a prime and let G be a finite group which is generated by the set G p of its p -elements. We show that if G is solvable and not a p -group, then the minimal number σ p …

hu, es (code pays fourni par la source)

Fixed point ratios, Sylow numbers and coverings of $p$-elements in finite groups

Robert M. Guralnick, Attila Maróti, Juan Martínez Madrid, Alexander Moretó et autres

Fixed point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime $p$ and a finite group $G$, we use fixed point ratios to …