dc.contributor.author | Alabdali, AA | |
dc.contributor.author | Byott, NP | |
dc.date.accessioned | 2017-09-22T10:23:05Z | |
dc.date.issued | 2017-09-21 | |
dc.description.abstract | We investigate Hopf-Galois structures on a cyclic field extension L/K of squarefree degree n. By a result of Greither and Pareigis, each such Hopf-Galois structure corresponds to a group of order n, whose isomorphism class we call the type of the Hopf-Galois structure. We show that every group of order n can occur, and we determine the number of Hopf-Galois structures of each type. We then express the total number of Hopf-Galois structures on L/K as a sum over factorisations of n into three parts. As examples, we give closed expressions for the number of Hopf-Galois structures on a cyclic extension whose degree is a product of three distinct primes. (There are several cases, depending on congruence conditions between the primes.) We also consider one case where the degree is a product of four primes. | en_GB |
dc.description.sponsorship | The first-named author acknowledges support from The Higher Committee for Education Development in Iraq. | en_GB |
dc.identifier.citation | Published online 21 September 2017 | en_GB |
dc.identifier.doi | 10.1016/j.jalgebra.2017.09.009 | |
dc.identifier.uri | http://hdl.handle.net/10871/29476 | |
dc.language.iso | en | en_GB |
dc.publisher | Elsevier for Academic Press | en_GB |
dc.rights.embargoreason | Publisher policy | en_GB |
dc.rights | © 2017 Elsevier Inc. All rights reserved. | en_GB |
dc.subject | Hopf-Galois structures | en_GB |
dc.subject | field extensions | en_GB |
dc.subject | groups of squarefree order | en_GB |
dc.title | Counting Hopf-Galois structures on cyclic field extensions of squarefree degree | en_GB |
dc.type | Article | en_GB |
dc.identifier.issn | 0021-8693 | |
dc.description | This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record. | en_GB |
dc.identifier.journal | Journal of Algebra | en_GB |