C. Quadrelli

activity

20122026

most citedThe Kummerian Property and Maximal Pro-

p

Galois Groups

26 citations · 154 across the 26 of their papers we have counts for

collaborators

27 papers

math.NT2026

A cohomological translation of the Kaplansky radical for profinite groups

Simone Blumer, Julian Feuerpfeil, Lucas Correa Lopes +1

The Kaplansky radical of a field consists of the nonzero elements represented by every norm quadratic form in two variables. D. Kijima and M. Nishi conjectured that, for quadratic…

math.GR2026

Variations of Demushkin Groups that are not Absolute Galois Groups

Simone Blumer, Claudio Quadrelli

We construct two families of examples of pro-p groups, with rather elementary presentations, that do not complete into 1-cyclotomic oriented pro-p groups. These provide brand new e…

math.GR2025

Droms Theorems for twisted right-angled Artin groups

Simone Blumer, Islam Foniqi, Claudio Quadrelli

We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence…

math.GR2024

Digraphs, pro- $p$ groups and Massey products in Galois cohomology

Claudio Quadrelli

Let $p$ be a prime. We characterize the oriented right-angled Artin pro- $p$ groups whose $F_{p}$ -cohomology algebra yields no essential $n$ -fold Massey products for every $n…

math.GR2024

Directed graphs, Frattini-resistance, and maximal pro- $p$ Galois groups

Claudio Quadrelli

Let $p$ be a prime. Following Snopce-Tanushevski, a pro- $p$ group $G$ is called Frattini-resistant if the function $H \mapsto Φ (H)$ , from the poset of all closed finitely-generated s…

math.NT2023

Massey products in Galois cohomology and Pythagorean fields

Claudio Quadrelli

We prove that a strengthened version of Minac-Tan's Massey Vanishing Conjecture holds true for fields with a finite number of square classes whose maximal pro- $2$ Galois group is o…

math.NT2023★ 4 cited

Oriented right-angled Artin pro- $ℓ$ groups and maximal pro- $ℓ$ Galois groups

Simone Blumer, Claudio Quadrelli, Thomas S. Weigel

For a prime number $ℓ$ we introduce and study oriented right-angled Artin pro- $ℓ$ groups $G_{Γ, λ}$ (oriented pro- $ℓ$ RAAGs for short) associated to a finite oriented graph…

math.NT2022★ 5 cited

Massey products in Galois cohomology and the Elementary Type Conjecture

Claudio Quadrelli

Let $p$ be a prime. We prove that a positive solution to Efrat's Elementary Type Conjecture implies a positive solution to the strengthened version of Minač--Tân's Massey Vanishing…

math.GR2021★ 11 cited

Groups of p-absolute Galois type that are not absolute Galois groups

Simone Blumer, Alberto Cassella, Claudio Quadrelli

Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam-Liu-Sharifi-Wake-Wang. We prove that the pro-p completion of the right-angled Artin group assoc…

math.GR2021★ 5 cited

Mild pro-p groups and the Koszulity conjectures

Jan Minac, Federico Pasini, Claudio Quadrelli +1

Let $p$ be a prime, and $F_{p}$ the field with $p$ elements. We prove that if $G$ is a mild pro- $p$ group with quadratic $F_{p}$ -cohomology algebra $H^\bullet(G,\math…

math.GR2021★ 3 cited

Chasing maximal pro-p Galois groups via 1-cyclotomicity

Claudio Quadrelli

Let $p$ be a prime. We prove that certain amalgamated free pro- $p$ products of Demushkin groups with pro- $p$ -cyclic amalgam cannot give rise to a 1-cyclotomic oriented pro- $p$ grou…

math.GR2021★ 6 cited

Oriented pro- $ℓ$ groups with the Bogomolov-Positselski property

Claudio Quadrelli, Thomas S. Weigel

For a prime number $ℓ$ we say that an oriented pro- $ℓ$ group $(G, θ)$ has the Bogomolov-Positselski property if the kernel of the canonical projection on its maximal $θ$ -abeli…

math.NT2020★ 4 cited

Two families of pro-p groups that are not absolute Galois groups

Claudio Quadrelli

Let $p$ be a prime. We produce two new families of pro- $p$ groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of ab…

math.GR2020

Integrals of groups II

João Araújo, Peter J. Cameron, Carlo Casolo +2

An $in t e g r a l$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$ . This paper continues the investigation on integrals of groups started in the work arXiv:…

math.GR2020★ 7 cited

Galois-theoretic features for 1-smooth pro- $p$ groups

Claudio Quadrelli

Let $p$ be a prime. A pro- $p$ group $G$ is said to be 1-smooth if it can be endowed with a continuous representation $θ : G \to GL_{1} (Z_{p})$ such that every open…

math.GR2020★ 6 cited

Pro-p groups with few relations and Universal Koszulity

Claudio Quadrelli

Let $p$ be a prime. We show that if a pro- $p$ group with at most 2 defining relations has quadratic $F_{p}$ -cohomology, then such algebra is universally Koszul. This proves…

math.GR2019★ 6 cited

Right-angled Artin groups and enhanced Koszul properties

Alberto Cassella, Claudio Quadrelli

Let F be a finite field. We prove that the cohomology algebra with coefficients in F of a right-angled Artin group is a strongly Koszul algebra for every finite graph $Γ$ . Moreover…

math.GR2019★ 15 cited

On pro- $p$ groups with quadratic cohomology

Claudio Quadrelli, Ilir Snopce, Matteo Vannacci

The main purpose of this article is to study pro- $p$ groups with quadratic $F_{p}$ -cohomology algebra, i.e. $H^{∙}$ -quadratic pro- $p$ groups. Prime examples of such grou…

math.GR2019★ 4 cited

1-smooth pro-p groups and Bloch-Kato pro-p groups

Claudio Quadrelli

Let $p$ be a prime. A pro- $p$ group $G$ is said to be 1-smooth if it can be endowed with a homomorphism of pro- $p$ groups $G \to 1 + p Z_{p}$ satisfying a formal version of Hilbe…

math.NT2018★ 21 cited

Koszul algebras and quadratic duals in Galois cohomology

Jan Minac, Federico W. Pasini, Claudio Quadrelli +1

We investigate the Galois cohomology of finitely generated maximal pro- $p$ quotients of absolute Galois groups. Assuming the well-known conjectural description of these groups, we…

math.NT2017★ 26 cited

The Kummerian Property and Maximal Pro- $p$ Galois Groups

Ido Efrat, Claudio Quadrelli

For a prime number $p$ , we give a new restriction on pro- $p$ groups $G$ which are realizable as the maximal pro- $p$ Galois group $G_{F} (p)$ for a field $F$ containing a root of unity…

math.GR2016★ 3 cited

One relator maximal pro-p Galois groups and the Koszulity conjectures

Claudio Quadrelli

Let $p$ be a prime number and let $K$ be a field containing a root of 1 of order $p$ . If the absolute Galois group $G_{K}$ satisfies $dim H^{1} (G_{K}, F_{p}) < \infty$ and $\d…

math.GR2015★ 2 cited

Finite quotients of Galois pro- $p$ groups and rigid fields

Claudio Quadrelli

For a prime number $p$ , we show that if two certain canonical finite quotients of a finitely generated Bloch-Kato pro- $p$ group $G$ coincide, then $G$ has a very simple structure,…

math.GR2015

A group theoretical version of Hilbert's theorem 90

Claudio Quadrelli, Thomas Weigel

It is shown that for a normal subgroup $N$ of a group $G$ , $G / N$ cyclic, the kernel of the map $N^{ab} \to G^{ab}$ satisfies the classical Hilbert 90 property (cf.…

A cohomological translation of the Kaplansky radical for profinite groups

Variations of Demushkin Groups that are not Absolute Galois Groups

Droms Theorems for twisted right-angled Artin groups

Digraphs, pro-p groups and Massey products in Galois cohomology

Directed graphs, Frattini-resistance, and maximal pro-p Galois groups

Massey products in Galois cohomology and Pythagorean fields

Oriented right-angled Artin pro-ℓ groups and maximal pro-ℓ Galois groups

Massey products in Galois cohomology and the Elementary Type Conjecture

Groups of p-absolute Galois type that are not absolute Galois groups

Mild pro-p groups and the Koszulity conjectures

Chasing maximal pro-p Galois groups via 1-cyclotomicity

Oriented pro-ℓ groups with the Bogomolov-Positselski property

Two families of pro-p groups that are not absolute Galois groups

Integrals of groups II

Galois-theoretic features for 1-smooth pro-p groups

Pro-p groups with few relations and Universal Koszulity

Right-angled Artin groups and enhanced Koszul properties

On pro-p groups with quadratic cohomology

1-smooth pro-p groups and Bloch-Kato pro-p groups

Koszul algebras and quadratic duals in Galois cohomology

The Kummerian Property and Maximal Pro-p Galois Groups

One relator maximal pro-p Galois groups and the Koszulity conjectures

Finite quotients of Galois pro-p groups and rigid fields

A group theoretical version of Hilbert's theorem 90

Digraphs, pro- $p$ groups and Massey products in Galois cohomology

Directed graphs, Frattini-resistance, and maximal pro- $p$ Galois groups

Oriented right-angled Artin pro- $ℓ$ groups and maximal pro- $ℓ$ Galois groups

Oriented pro- $ℓ$ groups with the Bogomolov-Positselski property

Galois-theoretic features for 1-smooth pro- $p$ groups

On pro- $p$ groups with quadratic cohomology

The Kummerian Property and Maximal Pro- $p$ Galois Groups

Finite quotients of Galois pro- $p$ groups and rigid fields