论文标题
在$ \ mathbb {q}的明确Galois组上（\ sqrt {a_ {1}}，\ sqrt {a_ {2}}，\ dots，\ sqrt {a_ {n}}}
On the explicit Galois group of $\mathbb{Q}(\sqrt{a_{1}}, \sqrt{a_{2}}, \dots, \sqrt{a_{n}}, ζ_{d})$ over $\mathbb{Q}$
论文作者
论文摘要
令$ s = \ {a_ {1}，a_ {2}，\ dots，a_ {n} \} $是非零整数的有限集。在\ cite {kbam21}中，Karthick Babu和Anirban Mukhopadhyay计算了多Quadratic Field $ \ Mathbb {Q} Galois组的明确结构\ sqrt {a_ {n}}）$ a $ \ mathbb {q} $。对于正整数$ d \ geq 3 $，$ζ_{d} $表示unity的原始$ d $ - th。在本文中，我们计算了$ \ mathbb {q}（\ sqrt {a_ {1}}}，\ sqrt {a_ {2}}，\ dots，\ sqrt，\ sqrt {a_ _ {n}}，qution qution的明确结构在$ζ_{d} $和$ \ sqrt {a_ {i}} $上的$ 1 \ leq i \ leq n $。
Let $S= \{ a_{1}, a_{2}, \dots, a_{n} \}$ be a finite set of non-zero integers. In \cite{KBAM21}, Karthick Babu and Anirban Mukhopadhyay calculated the explicit structure of the Galois group of multi-quadratic field $\mathbb{Q}(\sqrt{a_{1}}, \sqrt{a_{2}}, \dots, \sqrt{a_{n}})$ over $\mathbb{Q}$. For a positive integer $d \geq 3$, $ζ_{d}$ denotes the primitive $d$-th root of unity. In this paper, we calculate the explicit structure of the Galois group of $\mathbb{Q}(\sqrt{a_{1}}, \sqrt{a_{2}}, \dots, \sqrt{a_{n}}, ζ_{d})$ over $\mathbb{Q}$ in terms of its action on $ζ_{d}$ and $\sqrt{a_{i}}$ for $1 \leq i \leq n$.
