Hopf-Galois Structures of Squarefree Degree

Ali A. Alabdali; Nigel P. Byott

Hopf-Galois Structures of Squarefree Degree

Rings and Algebras 2019-10-22 v2

Authors: Ali A. Alabdali , Nigel P. Byott

Abstract

Let $n$ be a squarefree natural number, and let $G$ , $\Gamma$ be two groups of order $n$ . We determine the number of Hopf-Galois structures of type $G$ admitted by a Galois extension of fields with Galois group isomorphic to $\Gamma$ . We give some examples, including a full treatment of the case where $n$ is the product of three primes.

Keywords

Hopf-Galois structures squarefree degree Galois extension groups of order n field extension

Cite

@article{arxiv.1910.07811,
  title  = {Hopf-Galois Structures of Squarefree Degree},
  author = {Ali A. Alabdali and Nigel P. Byott},
  journal= {arXiv preprint arXiv:1910.07811},
  year   = {2019}
}