Urban Jezernik

activity

20122026

most citedBabai's conjecture for high-rank classical groups with random generators

13 citations · 23 across the 15 of their papers we have counts for

collaborators

22 papers

math.RT2026

Additive diameters and covering complexity of irreducible representations

Urban Jezernik, Špela Špenko

Let a group $G$ act linearly on a finite-dimensional complex vector space $V$ . The group-additive diameter of a subspace $U \leq V$ is the least number of translates of $U$ whose s…

math.RA2026

Random generation of the special linear Lie algebra over finite fields

Urban Jezernik, Andoni Zozaya

We prove that the special linear Lie algebra $sl_{n} (F_{q})$ over a finite field of characteristic $p$ is generated by two random elements with high probability as…

math.SP2026

Strong convergence of random representations of free products of finite groups

Marco Barbieri, Urban Jezernik

We extend the polynomial method of Chen--Garza-Vargas--Tropp--van Handel and Magee--Puder--van Handel for operator-norm bounds in random permutation models to the setting where tor…

math.RA2025

Diameter bounds for finite simple Lie algebras

Marco Barbieri, Urban Jezernik, Matevž Miščič

We prove strong and explicit diameter bounds for finite simple Lie algebras, which parallel Babai's conjecture for finite simple groups. Specifically, we show that any nonabelian f…

math.RT2025

Additive diameters of group representations

Urban Jezernik, Špela Špenko

We explore the concept of additive diameters in the context of group representations, unifying various noncommutative Waring-type problems. Given a finite-dimensional representatio…

math.RA2025

Random Lie bracket on $sl_{2} (F_{p})$

Urban Jezernik, Matevž Miščič

We study a random walk on the Lie algebra $sl_{2} (F_{p})$ where new elements are produced by randomly applying adjoint operators of two generators. Focusing on the…

math.RA2024

Two-generation of traceless matrices over finite fields

Omer Cantor, Urban Jezernik, Andoni Zozaya

We prove that the Lie algebra $sl_{n} (F_{q})$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when…

math.GR2021

On surjectivity of word maps on $PSL_{2}$

Urban Jezernik, Jonatan Sánchez

Let $w = [[x^{k}, y^{l}], [x^{m}, y^{n}]]$ be a non-trivial double commutator word. We show that $w$ is surjective on $PSL_{2} (K)$ , where $K$ is an algebraically closed field of cha…

math.GR2020★ 13 cited

Babai's conjecture for high-rank classical groups with random generators

Sean Eberhard, Urban Jezernik

Let $G = SCl_{n} (q)$ be a quasisimple classical group with $n$ large, and let $x_{1}, \dots, x_{k} \in G$ random, where $k \geq q^{C}$ . We show that the diameter of the resulting…

math.GR2018

Irrationality of generic quotient varieties via Bogomolov multipliers

Urban Jezernik, Jonatan Sánchez

The Bogomolov multiplier of a group is the unramified Brauer group associated to the quotient variety of a faithful representation of the group. This object is an obstruction for t…

math.GR2018

Gaps in probabilities of satisfying some commutator-like identities

Costantino Delizia, Urban Jezernik, Primoz Moravec +1

We show that there is a positive constant $δ < 1$ such that the probability of satisfying either the $2$ -Engel identity $[X_{1}, X_{2}, X_{2}] = 1$ or the metabelian identity $[[X_1, X_2]…

math.GR2017

Groups in which every non-nilpotent subgroup is self-normalizing

C. Delizia, U. Jezernik, P. Moravec +1

We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We completely describe th…

math.GR2016

Bogomolov multipliers of $p$ -groups of maximal class

Gustavo A. Fernández-Alcober, Urban Jezernik

Let $G$ be a $p$ -group of maximal class and order $p^{n}$ . We determine whether or not the Bogomolov multiplier $B_{0} (G)$ is trivial in terms of the lower central series of $G$ and $P…

math.GR2016★ 1 cited

Groups in which every non-abelian subgroup is self-normalized

Costantino Delizia, Urban Jezernik, Primoz Moravec +1

We study groups having the property that every non-abelian subgroup is equal to its normalizer. This class of groups is closely related to an open problem posed by Berkovich. We gi…

math.GR2016

Locally finite groups in which every non-cyclic subgroup is self-centralizing

Costantino Delizia, Urban Jezernik, Primoz Moravec +2

Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.

math.GR2015

Commutativity preserving extensions of groups

Urban Jezernik, Primoz Moravec

In parallel to the classical theory of central extensions of groups, we develop a version for extensions that preserve commutativity. It is shown that the Bogomolov multiplier is a…

math.GR2015

Units of group rings, the Bogomolov multiplier, and the fake degree conjecture

Javier Garcia-Rodriguez, Andrei Jaikin-Zapirain, Urban Jezernik

Let $π$ be a finite $p$ -group and $F_{q}$ a finite field with $q = p^{n}$ elements. Denote by $I_{F_{q}}$ the augmentation ideal of the group ring $\mathbb{F}_q[…

math.GR2013

Bogomolov multipliers of all groups of order 128

Urban Jezernik, Primož Moravec

This note is an implementation of the algorithm for computing Bogomolov multipliers as given in \cite{Mor11} in combination with \cite{Eic08} to effectively determine the multiplie…

math.GR2013

Universal commutator relations, Bogomolov multipliers, and commuting probability

Urban Jezernik, Primoz Moravec

Let $G$ be a finite $p$ -group. We prove that whenever the commuting probability of $G$ is greater than $(2 p^{2} + p - 2) / p^{5}$ , the unramified Brauer group of the field of $G$ -invaria…

math.GR2013★ 8 cited

Groups in which every non-cyclic subgroup contains its centralizer

Costantino Delizia, Urban Jezernik, Primož Moravec +1

We study groups having the property that every non-cyclic subgroup contains its centralizer. The structure of nilpotent and supersolvable groups in this class is described. We also…

math.GR2013

Schur multipliers of unitriangular groups

Urban Jezernik

An explicit formula for the Schur multiplier of the group of unitriangular matrices over products of cyclic rings $\ZZ/m\ZZ$ and $\ZZ$ is derived. We use it to provide presentation…

math.GR2012★ 1 cited

On p-central groups

Urban Jezernik

We extend the notion of free $p$ -central groups for odd primes $p$ to the case $p = 2$ by introducing a variant of the lower $p$ -central series. This enables us to calculate Schur mu…

Additive diameters and covering complexity of irreducible representations

Random generation of the special linear Lie algebra over finite fields

Strong convergence of random representations of free products of finite groups

Diameter bounds for finite simple Lie algebras

Additive diameters of group representations

Random Lie bracket on sl2​(Fp​)

Two-generation of traceless matrices over finite fields

On surjectivity of word maps on PSL2​

Babai's conjecture for high-rank classical groups with random generators

Irrationality of generic quotient varieties via Bogomolov multipliers

Gaps in probabilities of satisfying some commutator-like identities

Groups in which every non-nilpotent subgroup is self-normalizing

Bogomolov multipliers of p-groups of maximal class

Groups in which every non-abelian subgroup is self-normalized

Locally finite groups in which every non-cyclic subgroup is self-centralizing

Commutativity preserving extensions of groups

Units of group rings, the Bogomolov multiplier, and the fake degree conjecture

Bogomolov multipliers of all groups of order 128

Universal commutator relations, Bogomolov multipliers, and commuting probability

Groups in which every non-cyclic subgroup contains its centralizer

Schur multipliers of unitriangular groups

On p-central groups

Random Lie bracket on $sl_{2} (F_{p})$

On surjectivity of word maps on $PSL_{2}$

Bogomolov multipliers of $p$ -groups of maximal class