Daniel Gil-Muñoz

activity

20192025

most citedInduced Hopf Galois Structures and their Local Hopf Galois Modules

3 citations · 4 across the 9 of their papers we have counts for

collaborators

11 papers

math.NT2025

Hopf-Galois module structure of monogenic orders in cubic number fields

Daniel Gil-Muñoz

For a cubic number field $L$ , we consider the $Z$ -order in $L$ of the form $Z [α]$ , where $α$ is a root of a polynomial of the form $x^{3} - a x + b$ and $a,b\in\mathbb{Z…

math.NT2024

Hopf-Galois module structure of degree p extensions of p-adic fields

Daniel Gil-Muñoz

Let $p$ be an odd prime number. For a degree $p$ extension of $p$ -adic fields $L / K$ , we give a complete characterization of the condition for the ring of integers $O_{L}$ t…

math.NT2023

A generalization of Kummer theory to Hopf-Galois extensions

Daniel Gil-Muñoz

We introduce a condition for Hopf-Galois extensions that generalizes the notion of Kummer Galois extension. Namely, an $H$ -Galois extension $L / K$ is $H$ -Kummer if $L$ can be genera…

math.GR2023

Determining skew left braces of size np

Teresa Crespo, Daniel Gil-Muñoz, Anna Rio +1

We define the twofold semidirect product of two skew left braces, in which both the additive and multiplicative groups are semidirect products of the corresponding groups of the gi…

math.NT2022★ 1 cited

Additive structure of non-monogenic simplest cubic fields

Daniel Gil-Muñoz, Magdaléna Tinková

We consider Shanks' simplest cubic fields $K$ for which the index $[O_{K} : Z [ρ]]$ of a root $ρ$ of the defining parametric polynomial is $3$ . For them, we study the…

math.NT2022

Inducing braces and Hopf Galois structures

Teresa Crespo, Daniel Gil-Muñoz, Anna Rio +1

Let $p$ be a prime number and let $n$ be an integer not divisible by $p$ and such that every group of order $n p$ has a normal subgroup of order $p$ . (This holds in particular for $…

math.NT2022

The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure

Daniel Gil-Muñoz

For an odd prime number $p$ , we consider degree $p$ extensions $L / K$ of $p$ -adic fields with normal closure $L$ such that the Galois group of $L / K$ is the d…

math.GR2022

Left braces of size 8p

Teresa Crespo, Daniel Gil-Muñoz, Anna Rio +1

We describe all left braces of size 8p for p an odd prime different from 3 or 7 and validate the number given by Bardakov, Neschadim and Yadav. We give a characterization for isomo…

math.NT2021

Hopf-Galois module structure of quartic Galois extensions of $Q$

Daniel Gil-Muñoz, Anna Rio

Given a quartic Galois extension $L / Q$ of number fields and a Hopf-Galois structure $H$ on $L / Q$ , we study the freeness of the ring of integers $O_{L}$ as…

math.NT2020

Hopf Galois module structure of dihedral degree $2 p$ extensions of $Q_{p}$

Daniel Gil-Muñoz, Anna Rio

Let $p$ be an odd prime. For field extensions $L / Q_{p}$ with Galois group isomorphic to the dihedral group $D_{2 p}$ of order $2 p$ , we consider the problem of computing a bas…

math.NT2019★ 3 cited

Induced Hopf Galois Structures and their Local Hopf Galois Modules

Daniel Gil-Muñoz, Anna Rio

The regular subgroup determining an induced Hopf Galois structure for a Galois extension $L / K$ is obtained as the direct product of the corresponding regular groups of the inducing…

Hopf-Galois module structure of monogenic orders in cubic number fields

Hopf-Galois module structure of degree p extensions of p-adic fields

A generalization of Kummer theory to Hopf-Galois extensions

Determining skew left braces of size np

Additive structure of non-monogenic simplest cubic fields

Inducing braces and Hopf Galois structures

The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure

Left braces of size 8p

Hopf-Galois module structure of quartic Galois extensions of Q

Hopf Galois module structure of dihedral degree 2p extensions of Qp​

Induced Hopf Galois Structures and their Local Hopf Galois Modules

Hopf-Galois module structure of quartic Galois extensions of $Q$

Hopf Galois module structure of dihedral degree $2 p$ extensions of $Q_{p}$