Weakly Kronecker equivalent number fields
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Manfred Lochter (1994)
Acta Arithmetica
Takashi Fukuda, Keiichi Komatsu (2010)
Journal de Théorie des Nombres de Bordeaux
Let denote the class number of -th layer of the cyclotomic -extension of . Weber proved that is odd and Horie proved that is not divisible by a prime number satisfying . In a previous paper, the authors showed that is not divisible by a prime number less than . In this paper, by investigating properties of a special unit more precisely, we show that is not divisible by a prime number less than . Our argument also leads to the conclusion that is not divisible by a prime number...
F. Lemmermeyer (2013)
Mathematica Bohemica
In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.
Alfred Czogała, Beata Rothkegel (2014)
Acta Arithmetica
Let K be a number field. Assume that the 2-rank of the ideal class group of K is equal to the 2-rank of the narrow ideal class group of K. Moreover, assume K has a unique dyadic prime and the class of is a square in the ideal class group of K. We prove that if ₁,...,ₙ are finite primes of K such that ∙ the class of is a square in the ideal class group of K for every i ∈ 1,...,n, ∙ -1 is a local square at for every nondyadic , then ₁,...,ₙ is the wild set of some self-equivalence of the field...
P. E. Conner, R. Perlis, K. Szymiczek (1997)
Acta Arithmetica
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