G. Fernández-Alcober

activity

20072024

most citedOn the asymptotic behaviour of the number of Beauville and non-Beauville

p

-groups

4 citations · 9 across the 10 of their papers we have counts for

collaborators

15 papers

math.GR2024

Conciseness on normal subgroups and new concise words from outer commutator words

Gustavo A. Fernandez-Alcober, Matteo Pintonello

Let $w = w (x_{1}, \dots, x_{r})$ be an outer commutator word. We show that the word $w (u_{1}, \dots, u_{r})$ is concise whenever $u_{1}, \dots, u_{r}$ are non-commutator words in disjoint sets of v…

math.GR2019

Commutators in finite p-groups with 3-generator derived subgroup

Iker de las Heras

It is well known that, in general, the set of commutators of a group $G$ may not be a subgroup. Guralnick showed that if $G$ is a finite $p$ -group with $p \geq 5$ such that $G^{'}$ is a…

math.GR2018★ 4 cited

On the asymptotic behaviour of the number of Beauville and non-Beauville $p$ -groups

Gustavo A. Fernández-Alcober, Şükran Gül, Matteo Vannacci

We find asymptotic lower bounds for the numbers of both Beauville and non-Beauville $2$ -generator finite $p$ -groups of a fixed order, which turn out to coincide with the best known…

math.GR2018

Engel elements in some fractal groups

Gustavo A. Fernández-Alcober, Albert Garreta, Marialaura Noce

Let $p$ be a prime and let $G$ be a subgroup of a Sylow pro- $p$ subgroup of the group of automorphisms of the $p$ -adic tree. We prove that if $G$ is fractal and $|G':\mathrm{st}_G(…

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…

math.GR2016

On self-similar finite $p$ -groups

Azam Babai, Khadijeh Fathalikhani, Gustavo A. Fernandez-Alcober +1

In this paper, we address the following question: when is a finite $p$ -group $G$ self-similar, i.e. when can $G$ be faithfully represented as a self-similar group of automorphisms…