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Keywords:
cyclic quartic field; cyclotomic $\mathbb Z_2$-extension; 2-Iwasawa module; 2-class group; 2-rank
cyclic quartic field; cyclotomic $\mathbb Z_2$-extension; 2-Iwasawa module; 2-class group; 2-rank
Summary:
Let $K$ be an imaginary cyclic quartic number field whose 2-class group is of type $(2, 2, 2)$, i.e., isomorphic to $\mathbb {Z}/2\mathbb {Z}\times \mathbb {Z}/2\mathbb {Z}\times \mathbb {Z}/2\mathbb {Z}$. The aim of this paper is to determine the structure of the Iwasawa module of the genus field $K^{(*)}$ of $K$.
References:
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