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arXiv · 2402.12547

On the number of quaternion and dihedral braces and Hopf--Galois structures

Nigel P. Byott·Fabio Ferri
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Abstract

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.

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Nigel P. Byott, Fabio Ferri. 2024-02-19. On the number of quaternion and dihedral braces and Hopf--Galois structures. https://arxiv.org/abs/2402.12547

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