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

Yoko Inoue, and Kaori Ota. "Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients." Acta Arithmetica 169.2 (2015): 101-114. <http://eudml.org/doc/286519>.

@article{YokoInoue2015,
abstract = {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.},
author = {Yoko Inoue, Kaori Ota},
journal = {Acta Arithmetica},
keywords = {index of number fields; cyclotomic -extension; Fermat quotient},
language = {eng},
number = {2},
pages = {101-114},
title = {Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients},
url = {http://eudml.org/doc/286519},
volume = {169},
year = {2015},
}

TY - JOUR
AU - Yoko Inoue
AU - Kaori Ota
TI - Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients
JO - Acta Arithmetica
PY - 2015
VL - 169
IS - 2
SP - 101
EP - 114
AB - 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.
LA - eng
KW - index of number fields; cyclotomic -extension; Fermat quotient
UR - http://eudml.org/doc/286519
ER -