Hopf Galois structures on symmetric and alternating extensions
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 w...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/124086 |
| Acceso en línea: | https://hdl.handle.net/2117/124086 |
| Access Level: | acceso abierto |
| Palabra clave: | Field theory (Physics) Rings (Algebra) Teoria de camps (física) Anells (Àlgebra) Classificació AMS::12 Field theory and polynomials::12F Field extensions Classificació AMS::13 Commutative rings and algebras::13B Ring extensions and related topics Classificació AMS::16 Associative rings and algebras::16R Rings with polynomial identity Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Anells i àlgebres |
| Sumario: | 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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