On the number of quaternion and dihedral braces and Hopf--Galois structures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913315414867968 |
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| author | Byott, Nigel P. Ferri, Fabio |
| author_facet | Byott, Nigel P. Ferri, Fabio |
| contents | We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a similar result where the multiplicative group is dihedral. We also enumerate Hopf-Galois structures of abelian type on Galois extensions with generalised quaternion or dihedral Galois group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the number of quaternion and dihedral braces and Hopf--Galois structures Byott, Nigel P. Ferri, Fabio Rings and Algebras Group Theory Number Theory 20N99 (Primary) 16T05, 12F10, 16T25 (Secondary) We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a similar result where the multiplicative group is dihedral. We also enumerate Hopf-Galois structures of abelian type on Galois extensions with generalised quaternion or dihedral Galois group. |
| title | On the number of quaternion and dihedral braces and Hopf--Galois structures |
| topic | Rings and Algebras Group Theory Number Theory 20N99 (Primary) 16T05, 12F10, 16T25 (Secondary) |
| url | https://arxiv.org/abs/2402.12547 |