Hopf-Galois structures on separable field extensions of degree $pq$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909132873793536 |
|---|---|
| author | Darlington, Andrew |
| author_facet | Darlington, Andrew |
| contents | In 2020, Alabdali and Byott described the Hopf-Galois structures arising on Galois field extensions of squarefree degree. Extending to squarefree separable, but not necessarily normal, extensions $L/K$ is a natural next step. One must consider now the interplay between two Galois groups $G=\operatorname{Gal}(E/K)$ and $G'=\operatorname{Gal}(E/L)$, where $E$ is the Galois closure of $L/K$. In this paper, we give a characterisation and enumeration of the Hopf-Galois structures arising on separable extensions of degree $pq$ where $p$ and $q$ are distinct odd primes. This work includes the results of Byott and Martin-Lyons who do likewise for the special case that $p=2q+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11229 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hopf-Galois structures on separable field extensions of degree $pq$ Darlington, Andrew Group Theory Number Theory 12F10, 16T05 In 2020, Alabdali and Byott described the Hopf-Galois structures arising on Galois field extensions of squarefree degree. Extending to squarefree separable, but not necessarily normal, extensions $L/K$ is a natural next step. One must consider now the interplay between two Galois groups $G=\operatorname{Gal}(E/K)$ and $G'=\operatorname{Gal}(E/L)$, where $E$ is the Galois closure of $L/K$. In this paper, we give a characterisation and enumeration of the Hopf-Galois structures arising on separable extensions of degree $pq$ where $p$ and $q$ are distinct odd primes. This work includes the results of Byott and Martin-Lyons who do likewise for the special case that $p=2q+1$. |
| title | Hopf-Galois structures on separable field extensions of degree $pq$ |
| topic | Group Theory Number Theory 12F10, 16T05 |
| url | https://arxiv.org/abs/2303.11229 |