论文标题
某些多Qualdratic数字字段和$ 2 $级组的单位组
Unit groups of some multiquadratic number fields and $2$-class groups
论文作者
论文摘要
令$ p \ equiv -q \ equiv 5 \ pmod 8 $为两个主要整数。在本文中，我们研究了字段的单位组$ l_1 = \ mathbb {q}（\ sqrt 2，\ sqrt {p}，\ sqrt {q}，\ sqrt {-1}）$ \ sqrt {q}）$。此外，我们给出了$ L_1 $的第二个$ 2 $类别组，以及该字段的$ 2 $ -CLASS组$ l_n = \ Mathbb {Q}（\ sqrt {p}，\ sqrt {p}，\ sqrt {q} {q}，{q}，^________________ {2^n+2}}
Let $p\equiv -q \equiv 5\pmod 8$ be two prime integers. In this paper, we investigate the unit groups of the fields $ L_1 =\mathbb{Q}(\sqrt 2, \sqrt{p}, \sqrt{q}, \sqrt{-1} )$ and $ L_1^+=\mathbb{Q}(\sqrt 2, \sqrt{p}, \sqrt{q} )$. Furthermore , we give the second $ 2$-class groups of the subextensions of $L_1$ as well the $2$-class groups of the fields $ L_n =\mathbb{Q}( \sqrt{p}, \sqrt{q}, ζ_{2^{n+2}} )$ and their maximal real subfelds.
