Hopf–Galois structures on Galois field extensions of degree pq

We determine all Hopf–Galois structures on a Galois extension of fields of degree pq, where p, q are primes with p≡1 ( mod q) . There are 2 q−1, respectively 2+ p(2 q−3), Hopf–Galois structures when the extension is cyclic, respectively nonabelian. Explicit generators are given for the groups of per...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2004-04, Vol.188 (1), p.45-57
Main Author: Byott, Nigel P.
Format: Article
Language:English
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Summary:We determine all Hopf–Galois structures on a Galois extension of fields of degree pq, where p, q are primes with p≡1 ( mod q) . There are 2 q−1, respectively 2+ p(2 q−3), Hopf–Galois structures when the extension is cyclic, respectively nonabelian. Explicit generators are given for the groups of permutations corresponding to these Hopf–Galois structures.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2003.10.010