An Infinite Family of Number Fields with Given Indices

In this paper, for any rational prime p and for a fixed positive integer \(\nu _p\) ${\nu }_p$ , we provide infinite families of number fields K satisfying \(\nu _p(i(K))=\nu _p\) ${\nu }_p(i(K))={\nu }_p$ . As an application, if \(i(K)\ne 1\) $i(K)\ne 1$ , then K is not monogenic. We illustrate our results by some computational examples.