M. Noce

activity

20182022

most citedAlgorithmic problems in Engel groups and cryptographic applications

1 citations · 3 across the 10 of their papers we have counts for

collaborators

14 papers

math.GR2022

Upper bounds for the product of element orders of finite groups

Elena Di Domenico, Carmine Monetta, Marialaura Noce

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…

cs.CR2022★ 1 cited

The root extraction problem in braid group-based cryptography

María Cumplido, Delaram Kahrobaei, Marialaura Noce

The root extraction problem in braid groups is the following: given a braid $β \in B_{n}$ and a number $k \in N$ , find $α \in B_{n}$ such that $α^{k} = β$ . In the…

math.GR2022

Tree languages and branched groups

Laurent Bartholdi, Marialaura Noce

We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize reg…

cs.CR2022

Group-based Cryptography in the Quantum Era

Delaram Kahrobaei, Ramón Flores, Marialaura Noce

In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been pr…

math.GR2021

Ramification structures for quotients of the Grigorchuk groups

Marialaura Noce, Anitha Thillaisundaram

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…

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.GR2020

Locally finite $p$ -groups with a left 3-Engel element whose normal closure is not nilpotent

Anastasia Hadjievangelou, Marialaura Noce, Gunnar Traustason

For any odd prime $p$ , we give an example of a locally finite $p$ -group $G$ containing a left 3-Engel element $x$ where $⟨ x ⟩^{G}$ is not nilpotent.

math.GR2020

A family of fractal non-contracting weakly regular branch groups

Marialaura Noce

We construct a new family of groups that is non-contracting and weakly regular branch over the derived subgroup. This gives the first example of an infinite family of groups acting…

math.GR2020★ 1 cited

Algorithmic problems in Engel groups and cryptographic applications

Delaram Kahrobaei, Marialaura Noce

The theory of Engel groups plays an important role in group theory since these groups are closely related to the Burnside problems. In this survey we consider several classical and…

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.GR2019

Hausdorff dimension of the second Grigorchuk group

Marialaura Noce, Anitha Thillaisundaram

We show that the Hausdorff dimension of the closure of the second Grigorchuk group is 43/128. Furthermore we establish that the second Grigorchuk group is super strongly fractal an…

math.GR2018

A left $3$ -Engel element whose normal closure is not nilpotent

Marialaura Noce, Gareth M. Tracey, Gunnar Traustason

We give an example of a locally nilpotent group $G$ containing a left $3$ -Engel element $x$ where $⟨ x ⟩^{G}$ is not nilpotent.

math.GR2018★ 1 cited

A note on Engel elements in the first Grigorchuk group

Marialaura Noce, Antonio Tortora

Let $Γ$ be the first Grigorchuk group. According to a result of Bartholdi, the only left Engel elements of $Γ$ are the involutions. This implies that the set of left Engel elements…