论文标题
$ 2 $ $ torsion的多Quipadratic领域的$ 2 $转换
A sharp upper bound for the $2$-torsion of class groups of multiquadratic fields
论文作者
论文摘要
令$ k $为$ \ mathbb {q} $的多Quadratic扩展名，让$ \ text {cl}^{+}（k）$是其狭窄的类组。最近，作者\ cite {kp}对$ | \ text {cl}^{+}（k）（k）[2] | $仅在$ k $的程度和刺激刺激的数量方面进行了绑定。在目前的工作中，我们表明，在许多情况下，这种界限是锋利的。此外，我们将其扩展到射线类组。
Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let $\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP} gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and the number of ramifying primes. In the present work we show that this bound is sharp in a wide number of cases. Furthermore, we extend this to ray class groups.
