Exercise 2, § 2

The polynomial $X^3 - 2$ of $\mathbf{Q}[X]$ is irreducible; let $E$ be a splitting field of this polynomial (V, p. 21) and let $F$ be the field generated by a single one of the roots of this polynomial in $E$. Show that two composite extensions of $E$ and $F$ are always isomorphic qua extensions of $E$ but not qua composite extensions. \*