Hopf-Galois structures on separable field extensions of degree related to Cunningham chains
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909723488419840 |
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| author | Darlington, Andrew |
| author_facet | Darlington, Andrew |
| contents | The past few years have seen Hopf--Galois structures on extensions of squarefree degree studied in various contexts. The Galois case was fully explored by Alabdali and Byott in 2020, followed by a first attempt at generalising these results to include non-normal extensions by Byott and Martin-Lyons; their work looks at separable extensions of degree $pq$ with $p,q$ distinct odd primes, and $p=2q+1$. This paper extends the latter work further by considering separable extensions of squarefree degree $n=p_1...p_m$ where each pair of consecutive primes $p_i,p_{i+1}$ are related by $p_i=2p_{i+1}+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hopf-Galois structures on separable field extensions of degree related to Cunningham chains Darlington, Andrew Group Theory 20B05 The past few years have seen Hopf--Galois structures on extensions of squarefree degree studied in various contexts. The Galois case was fully explored by Alabdali and Byott in 2020, followed by a first attempt at generalising these results to include non-normal extensions by Byott and Martin-Lyons; their work looks at separable extensions of degree $pq$ with $p,q$ distinct odd primes, and $p=2q+1$. This paper extends the latter work further by considering separable extensions of squarefree degree $n=p_1...p_m$ where each pair of consecutive primes $p_i,p_{i+1}$ are related by $p_i=2p_{i+1}+1$. |
| title | Hopf-Galois structures on separable field extensions of degree related to Cunningham chains |
| topic | Group Theory 20B05 |
| url | https://arxiv.org/abs/2508.03384 |