G. A. Fern'andez-Alcober

activity

20112025

collaborators

5 papers

math.GR2025

Profinite groups with complemented closed subgroups

Gustavo A. Fernández-Alcober, Giulia Sabatino

A group $G$ is said to be a $C$ -group if every subgroup $H$ has a permutable complement, i.e. if there exists a subgroup $K$ of $G$ such that $G = H K$ and $H \cap K = 1$ . In this paper…

math.GR2024

On the lower central series of a large family of non-periodic GGS-groups

Gustavo A. Fernández-Alcober, Mikel E. Garciarena, Marialaura Noce

For an odd prime $p$ , we determine the lower central series of a large family of non-periodic GGS-groups, which has a density of roughly $(\frac{p - 1}{p})^{2}$ within all GGS-groups.…

math.GR2023

Conciseness on normal subgroups and new concise words from lower central and derived words

Gustavo A. Fernández-Alcober, Matteo Pintonello

Let $w = w (x_{1}, \dots, x_{r})$ be a lower central word or a derived 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 disj…

math.GR2022

GGS-groups over primary trees: Branch structures

Elena Di Domenico, Gustavo A. Fernández-Alcober, Norberto Gavioli

We study branch structures in Grigorchuk-Gupta-Sidki groups (GGS-groups) over primary trees, that is, regular rooted trees of degree $p^{n}$ for a prime $p$ . Apart from a small set o…

math.GR2011

Positive laws on large sets of generators: counterexamples for infinitely generated groups

C. Acciarri, G. A. Fernández-Alcober

Shumyatsky and the second author proved that if G is a finitely generated residually finite p-group satisfying a law, then, for almost all primes, the fact that a normal and commut…