On the explicit Galois group of Q(a1,a2,⋯,an,ζd) over Q.

Let S = { a 1 , a 2 , ⋯ , a n } be a finite set of non-zero integers. In [5], Karthick Babu and Anirban Mukhopadhyay calculated the explicit structure of the Galois group of multi-quadratic field Q (a 1 , a 2 , ⋯ , a n) over Q . For a positive integer d ⩾ 3 , ζ d denotes the primitive d-th root of unity. In this paper, we calculate the explicit structure of the Galois group of Q (a 1 , a 2 , ⋯ , a n , ζ d) over Q in terms of its action on ζ d and a i for 1 ⩽ i ⩽ n . [ABSTRACT FROM AUTHOR]