Remark on ''On normal integral bases'' (Q1065863)

We can easily extend Theorem 2 of [ibid. 7, 221-231 (1984; Zbl 0553.12001)] to the following theorem: Suppose that \(\ell\) is an odd prime and a \((\neq \pm 1)\) is a rational integer without \(\ell\)-th power factor such that \(a^{\ell -1}\equiv 1 mod \ell^ 2\). Then \({\mathbb{Q}}(\zeta_{\ell},^{\ell}\sqrt{a})/{\mathbb{Q}}(\zeta_{\ell})\) has always a normal integral basis.