Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Jezernik, Urban"'
We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when $(n, p)$ is $(3, 3)$ or $(4,2)$. In the latter cases, we establish cur
Externí odkaz:
http://arxiv.org/abs/2404.11240
Autor:
Jezernik, Urban, Sánchez, Jonatan
Let $w = [[x^k, y^l], [x^m, y^n]]$ be a non-trivial double commutator word. We show that $w$ is surjective on $\mathrm{PSL}_2(K)$, where $K$ is an algebraically closed field of characteristic $0$.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/2101.12534
Autor:
Eberhard, Sean, Jezernik, Urban
Let $G = \mathrm{SCl}_n(q)$ 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 Cayley graph is bounded by $q^2 n^{O(1)}$ with probability $1 - o(1)$.
Externí odkaz:
http://arxiv.org/abs/2005.09990
Autor:
Jezernik, Urban, Sánchez, Jonatan
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 the quotient variety to be stably rational. The purpose of this paper i
Externí odkaz:
http://arxiv.org/abs/1811.01851
We show that there is a positive constant $\delta < 1$ such that the probability of satisfying either the $2$-Engel identity $[X_1, X_2, X_2] = 1$ or the metabelian identity $[[X_1, X_2], [X_3, X_4]] = 1$ in a finite group is either $1$ or at most $\
Externí odkaz:
http://arxiv.org/abs/1809.02997
Autor:
Jezernik, Urban, Sánchez, Jonatan
Publikováno v:
In Journal of Algebra 1 December 2021 587:613-627
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 $P_1 = C_G(\gamma_2(G) / \gamma_4(G))$. If in addition $G$ has positive
Externí odkaz:
http://arxiv.org/abs/1609.03525
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 give a full classification of finite groups having the above property. W
Externí odkaz:
http://arxiv.org/abs/1607.07366
Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1606.01669
Autor:
Jezernik, Urban, Moravec, Primoz
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 universal object parametrising such extensions of a given group. Maxi
Externí odkaz:
http://arxiv.org/abs/1510.01536