al.
</p>
{{ toc }}
<h2 id="illustration">Illustration</h2>
<h3 id="concrete-example">Concrete Example</h3>
<p>
  Let \( L = \mathbb{Q}(\sqrt{2}, \sqrt{3}) \), \( K = \mathbb{Q} \),
  and \( M = \mathbb{Q}(\sqrt{2}) \).  Note that

  \begin{align*}
    L &= \{ a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6} : a, b, c, d \in \mathbb{Q} \}, \\
    M &= \{ k + l \sqrt{2} : k, l \in \mathbb{Q} \}.
  \end{align*}

  Now the group of \( K \)-automorphisms of \( L \) is

  \[
    K^* = \{\phi_1, \phi_2, \phi_3, \phi_4 \}
