Let $k\subset K$ be a Galois extension, i.e. $K=\langle{\xi}_{1}, {\xi}_{2},\ldots, {\xi}_{n}\rangle,$ $k\supset K=\{a_0+a_1{\xi}_{1}+\ldots+a_n{\xi}_{n}|a_0,\ldots,a_n\in k\}.$ Is it true that $\forall i~~\exists j:\sigma({\xi}_{i})={\xi}_{j},$ where $\sigma$ is any element of $\operatorname{Gal}{(K,k)}$. In other words, is it true that elements of $\operatorname{Gal}{(K,k)}$ relocate generators of $K$?
Thanks.