Galois correspondence

《代数学引论》 · 第 243 页

此时将 $G$ 限制到 $K$ 上就得到 $K/F$ 的伽罗瓦群，即 $\operatorname{Gal}(K/F)=G/H$。1）中的一一对应称为伽罗瓦对应。

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《The foundations of geometry》 · 第 350 页 · Chapter 15，Section 15.3「The Fundamental Theorem of Galois Theory」，Definition 15.27

Let $k\subseteq F$ be a field extension. The ‘Galois correspondence’ consists of the pair of functions $\{E\text{ field}\mid k\subseteq E\subseteq F\}\overset{\sigma}{\underset{\tau}{\rightleftarrows}}\{\text{subgroups of }\operatorname{Gal}_k(F)\}$ associating with each intermediate field $E$ the subgroup $\sigma(E)=\operatorname{Gal}_E(F)$ of $\operatorname{Gal}_k(F)$, and with each subgroup $G$ of $\operatorname{Gal}_k(F)$ the fixed field $\tau(G)=F^G$.