Compact Lie Groups
《Compact Lie Groups》 · 第 451 页 · Chapter 5「Insolvability of the Quintic」，Definition
Let $E$ be a field containing a subfield $k$. An automorphism of $E$ is an isomorphism $\sigma:E\to E$; we say that $\sigma$ fixes $k$ if $\sigma(a)=a$ for every $a\in k$.