The Golod–Shafarevich inequality and the class field tower problem

Autors/ores

Paraules clau:

number theory, class field tower problem, pro-p groups, Golod–Shafarevich inequality

Resum

En aquest article presentem una demostració del problema de la torre de cossos de classes. Comencem introduint els grups pro-p, expliquem com descriure’ls en termes de generadors i relacions, i presentem la desigualtat de Golod–Shafarevich, la qual estableix un criteri perquè un grup pro-p sigui infinit. Després d’introduir algunes nocions de teoria algebraica de nombres, apliquem la desigualtat de Golod–Shafarevich al problema de la torre de cossos de classes. Obtenim un criteri perquè un cos de nombres tingui una torre de cossos de classes infinita, i donem exemples explícits de cossos de nombres satisfent aquest criteri.

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Publicat

2024-01-26

Com citar

Vilà Casadevall, J. (2024). The Golod–Shafarevich inequality and the class field tower problem. Reports@SCM, 8(1), 1–10. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/151012

Número

Vol. 8 Núm. 1 (2023)

Secció

Articles

Llicència

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