L. Pyber

activity

20042023

most citedGrowth in finite simple groups of Lie type of bounded rank

71 citations · 151 across the 17 of their papers we have counts for

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15 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.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

Some simplifications in the proof of the Sims conjecture

László Pyber, Gareth Tracey

We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.

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

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…