Iker de las Heras

activity

20172026

most citedStrong conciseness of coprime commutators in profinite groups

3 citations · 3 across the 8 of their papers we have counts for

collaborators

8 papers

math.GR2026

Engel probability in wreath products of $p$ -groups

Iker de las Heras, Tommaso Toti, Matteo Vannacci

We give upper and lower bounds for the number of solutions of the equation $e_{n} (x, y) = g$ in the group $W_{k} = (C_{p} ≀ C_{p^{k}})^{2}$ , where $e_{n} (x, y)$ is the $n$ -th Engel word and $g\in…

math.GR2024

The lower $p$ -series of analytic pro- $p$ groups and Hausdorff dimension

Iker de las Heras, Benjamin Klopsch, Anitha Thillaisundaram

Let $G$ be a $p$ -adic analytic pro- $p$ group of dimension $d$ . We produce an approximate series which descends regularly in strata and whose terms deviate from the lower $p$ -series…

math.GR2024

On the lattice of closed subgroups of a profinite group

Francesco de Giovanni, Iker de las Heras, Marco Trombetti

The subgroup lattice of a group is a great source of information about the structure of the group itself. The aim of this paper is to use a similar tool for studying profinite grou…

math.GR2023★ 3 cited

Strong conciseness of coprime commutators in profinite groups

Iker de las Heras, Matteo Pintonello, Pavel Shumyatsky

Let $G$ be a profinite group. The coprime commutators $γ_{j}^{*}$ and $δ_{j}^{*}$ are defined as follows. Every element of $G$ is both a $γ_{1}^{*}$ -value and a $δ_{0}^{*}$ -value. For $j \geq 2$ , l…

math.GR2023

Powerful 3-Engel groups

Iker de las Heras, Marialaura Noce, Gunnar Traustason

In this paper we study powerful 3-Engel groups. In particular, we find sharp upper bounds for the nilpotency class of powerful 3-Engel groups and the subclass of powerful metabelia…

math.GR2022

The degree of commutativity of wreath products with infinite cyclic top group

Iker de las Heras, Benjamin Klopsch, Andoni Zozaya

The degree of commutativity of a finite group is the probability that two uniformly and randomly chosen elements commute. This notion extends naturally to finitely generated groups…

math.GR2021

A pro-2 group with full normal Hausdorff spectra

Iker de las Heras, Anitha Thillaisundaram

We construct a $2$ -generated pro- $2$ group with full normal Hausdorff spectrum $[0, 1]$ , with respect to each of the four standard filtration series: the $2$ -power series, the lower…

math.GR2017

Commutators in finite $p$ -groups with $2$ -generator derived subgroup

Iker de las Heras, Gustavo A. Fernández-Alcober

Let $G$ be a finite $p$ -group whose derived subgroup $G^{'}$ can be generated by $2$ elements. If $G^{'}$ is abelian, Guralnick proved that every element of $G^{'}$ is a commutator. In this…

Engel probability in wreath products of p-groups

The lower p-series of analytic pro-p groups and Hausdorff dimension