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• # Artykuł - szczegóły

## Acta Arithmetica

2015 | 169 | 2 | 101-114

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

EN

### Abstrakty

EN
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 $q^{p-1} ≡ 1 (mod p^{n+1})$, 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 a prime different from p are also considered.

101-114

wydano
2015

### Twórcy

autor
• Department of Mathematics, Tsuda College, 2-1-1 Tsuda-cho, Kodaira-shi, Tokyo 187-8577, Japan
autor
• Department of Mathematics, Tsuda College, 2-1-1 Tsuda-cho, Kodaira-shi, Tokyo 187-8577, Japan