Z. Halasi

activity

20072023

most citedA proof of Pyber's base size conjecture

26 citations · 60 across the 10 of their papers we have counts for

collaborators

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11 papers · 1 filter

math.GR2023

On $p$ -groups with a maximal elementary abelian normal subgroup of rank $k$

Zoltán Halasi, Károly Podoski, László Pyber +1

There are several results in the literature concerning $p$ -groups $G$ with a maximal elementary abelian normal subgroup of rank $k$ due to Thompson, Mann and others. Following an i…

math.GR2022

On the diameter of Cayley graphs of classical groups with generating sets containing a transvection

Martino Garonzi, Zoltán Halasi, Gábor Somlai

A well-known conjecture of Babai states that if $G$ is any finite simple group and $X$ is a generating set for $G$ , then the diameter of the Cayley graph $C a y (G, X)$ is bounded by $…

math.GR2020

Diameter of Cayley graphs of $S L (n, p)$ with generating sets containing a transvection

Zoltán Halasi

A well-known conjecture of Babai states that if $G$ is a finite simple group and $X$ is a generating set of $G$ , then the diameter of the Cayley graph $C a y (G, X)$ is bounded above b…

math.GR2019

Random bases for coprime linear groups

Hülya Duyan, Zoltán Halasi, Károly Podoski

The minimal base size $b (G)$ for a permutation group $G$ , is a widely studied topic in the permutation group theory. Z. Halasi and K. Podoski proved that $b (G) \leq 2$ for coprime l…

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

Base sizes of primitive groups: bounds with explicit constants

Zoltan Halasi, Martin W. Liebeck, Attila Maroti

We show that the minimal base size $b (G)$ of a finite primitive permutation group $G$ of degree $n$ is at most $2 (lo g ∣ G ∣/ lo g n) + 24$ . This bound is asymptotically best possibl…