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Teresa Crespo,
Anna Rio, and
Montserrat Vela
Hopf Galois structures on symmetric and
alternating extensions view print
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| Published: |
August 7, 2018 |
| Keywords: |
Hopf algebra, Hopf Galois theory, Galois correspondence. |
| Subject: |
Primary: 12F10; Secondary: 13B05, 16T05. |
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Abstract
By using a recent theorem by Koch, Kohl, Truman and Underwood on normality, we determine that some types of Hopf Galois structures do not occur on Galois extensions with Galois group isomorphic to alternating or symmetric groups. Our theory of induced Hopf Galois structures allows us to obtain the whole picture of types of Hopf Galois structures on A4-extensions, S4-extensions, and S5-extensions. Combining it with a result of Carnahan and Childs, we obtain a complete count of the Hopf Galois structures on S5-extensions.
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| Acknowledgements
T. Crespo acknowledges support by grants MTM2015-66716-P (MINECO/FEDER, UE) and 2017 SGR 1178. A. Rio and M. Vela acknowledge support by grants MTM2015-66180R (MINECO/FEDER, UE) and 2017 SGR 1216.
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| Author information
Teresa Crespo:
Departament de Matemátiques i Informática, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, E-08007 Barcelona, Spain
teresa.crespo@ub.edu
Anna Rio:
Departament de Matemátiques, Universitat Politécnica de Catalunya, C/Jordi Girona, 1-3 Edifici Omega, E-08034 Barcelona, Spain
ana.rio@upc.edu
Montserrat Vela:
Departament de Matemátiques, Universitat Politécnica de Catalunya, C/Jordi Girona, 1-3 Edifici Omega, E-08034 Barcelona, Spain
montse.vela@upc.edu
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