Displaying similar documents to “On p-class groups of cyclic extensions of prime degree p of certain cyclotomic fields.”

Kronecker-Weber via Stickelberger

Franz Lemmermeyer (2005)

Journal de Théorie des Nombres de Bordeaux

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In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.

Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients

Yoko Inoue, Kaori Ota (2015)

Acta Arithmetica

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We consider the indices of subfields of cyclotomic ℤₚ-extensions of number fields. For the nth layer Kₙ of the cyclotomic ℤₚ-extension of ℚ, we find that the prime factors of the index of Kₙ/ℚ are those primes less than the extension degree pⁿ which split completely in Kₙ. Namely, the prime factor q satisfies q p - 1 1 ( m o d p n + 1 ) , and this leads us to consider higher degree Fermat quotients. Indices of subfields of cyclotomic ℤₚ-extensions of a number field which is cyclic over ℚ with extension degree...