Hopf Galois structures on nonnormal extensions of degree pqw

We study Hopf Galois structures on separable field extensions (nonnormal) L/K such that the degree is square free pqw. The group permutation of degree pqw is G = Gal(E/K) where E/K is the normal closure of L/K. We investigate in details the cyclic case where q, w ≥ 3 and p = 2w + 1 are all square fr...

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Bibliographic Details
Main Authors: Jamal, Baraa Muthana, Alabdali, Ali A.
Format: Conference Proceeding
Language:English
Subjects:
Group theory
Permutations
Online Access:Get full text
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Summary:We study Hopf Galois structures on separable field extensions (nonnormal) L/K such that the degree is square free pqw. The group permutation of degree pqw is G = Gal(E/K) where E/K is the normal closure of L/K. We investigate in details the cyclic case where q, w ≥ 3 and p = 2w + 1 are all square free primes. We determine the group permutations G, then for each G we determine the Hopf Galois structures. There exists fifty four G such that the field extensions L/K admit the Hopf Galois structures in this case.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0161525