arXiv subjects

Elena Di Domenico

Publications and source records attributed to Elena Di Domenico.

5 recordsLinked to original sources

arXiv2023

Beauville structures for quotients of generalised GGS-groups

A finite group with a Beauville structure gives rise to a certain compact complex surface called a Beauville surface. Gül and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki (GGS-)groups that act on the $p$-adic tree, for $p$ an odd prime, admit Beauville structures. We extend their result by showing that quotients of infinite periodic GGS-groups acting on $p^n$-adic trees, for $p$ any prime and $n\ge 2$, also admit Beauville structures.

math.GR↗

arXiv2023

Upper bounds for the product of element orders of finite groups

Let $G$ be a finite group of order $n$, and denote by $ρ(G)$ the product of element orders of $G$. The aim of this work is to provide some upper bounds for $ρ(G)$ depending only on $n$ and on its least prime divisor, when $G$ belongs to some classes of non-cyclic groups.

math.GR↗

arXiv2022

Ramification structures for quotients of multi-EGS groups

Groups associated to surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. Gül and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, admit ramification structures. We extend their result by showing that quotients of generalisations of the GGS-groups, namely multi-EGS groups, also admit ramification structures.

math.GR↗

arXiv2022

GGS-groups over primary trees: Branch structures

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 of exceptions for $p=2$, we prove that all these groups are weakly regular branch over $G''$. Furthermore, in most cases they are actually regular branch over $γ_3(G)$. This is a significant extension of previously known results regarding periodic GGS-groups over primary trees and general GGS-groups in the case $n=1$. We also show that, as in the case $n=1$, a GGS-group generated by a constant vector is not branch.

math.GR↗

arXiv2021

$p$-Basilica groups

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 $p$-congruence subgroup property but not the congruence subgroup property nor the weak congruence subgroup property. This provides the first examples of weakly branch groups with such properties. In addition, the $p$-Basilica groups give the first examples of weakly branch, but not branch, groups which are super strongly fractal. We compute the orders of the congruence quotients of these groups, which enable us to determine the Hausdorff dimensions of the $p$-Basilica groups. Lastly, we show that the $p$-Basilica groups do not possess maximal subgroups of infinite index and that they have infinitely many non-normal maximal subgroups.

math.GR↗