Solution
= Solution
The <Galois group> $\operatorname{Gal}(L/K)$ is the <group> of all <field automorphisms> of $L$ fixing every element of $K$, with composition as its operation. A finite extension is a <Galois extension> if it is both normal and separable; equivalently, it is a splitting extension of separable polynomials, or its <group> has order $[L:K]$. Normality means that every <irreducible polynomial> over $K$ with a root in $L$ splits there.