G. A. Fern'andez-Alcober

activity

20112021

p

-groups of wild type and groups of maximal class

3 citations · 6 across the 6 of their papers we have counts for

collaborators

10 papers

math.GR2021

$p$ -Basilica groups

Elena Di Domenico, Gustavo A. Fernández-Alcober, Marialaura Noce +1

We consider a generalisation of the Basilica group to all odd primes: the $p$ -Basilica groups acting on the $p$ -adic tree. We show that the $p$ -Basilica groups have the $p$ -congrue…

math.GR2019

Engel elements in weakly branch groups

Gustavo A. Fernández-Alcober, Marialaura Noce, Gareth M. Tracey

We study properties of Engel elements in weakly branch groups, lying in the group of automorphisms of a spherically homogeneous rooted tree. More precisely, we prove that the set o…

math.GR2017★ 3 cited

Beauville $p$ -groups of wild type and groups of maximal class

Gustavo A. Fernández-Alcober, Norberto Gavioli, Şükran Gül +1

Let $G$ be a Beauville finite $p$ -group. If $G$ exhibits a `good behaviour' with respect to taking powers, then every lift of a Beauville structure of $G /Φ (G)$ is a Beauville struc…

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

On the congruence subgroup property for GGS-groups

Gustavo A. Fernández-Alcober, Alejandra Garrido, Jone Uria-Albizuri

We show that all GGS-groups with non-constant defining vector satisfy the congruence subgroup property. This provides, for every odd prime $p$ , many examples of finitely generated,…

math.GR2015

A note on automorphisms of finite $p$ -groups

Gustavo A. Fernández-Alcober, Anitha Thillaisundaram

Let $G$ be a finite non-cyclic $p$ -group of order at least $p^{3}$ . If $G$ has an abelian maximal subgroup, or if $G$ has an elementary abelian centre with $C_{G} (Z (Φ (G))) \neq = Φ (G)$ , t…

math.GR2015

Beauville structures in finite p-groups

Gustavo A. Fernández-Alcober, Şükran Gül

We study the existence of (unmixed) Beauville structures in finite $p$ -groups, where $p$ is a prime. First of all, we extend Catanese's characterisation of abelian Beauville groups…

math.GR2011★ 2 cited

GGS-groups: order of congruence quotients and Hausdorff dimension

Gustavo A. Fernández-Alcober, Amaia Zugadi-Reizabal

If G is a GGS-group defined over a p-adic tree, where p is an odd prime, we calculate the order of the congruence quotients $G_n=G/\Stab_G(n)$ for every n. If G is defined by the v…

math.GR2011

Positive laws on generators in powerful pro-p groups

Cristina Acciarri, Gustavo A. Fernández-Alcober

If G is a finitely generated powerful pro-p group satisfying a certain law v=1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we pr…

math.GR2011

A focal subgroup theorem for outer commutator words

Cristina Acciarri, Gustavo A. Fernández-Alcober, Pavel Shumyatsky

Let $G$ be a finite group of order $p^{a} m$ , where $p$ is a prime and $m$ is not divisible by $p$ , and let $P$ be a Sylow $p$ -subgroup of $G$ . If $w$ is an outer commutator word, we…

p-Basilica groups