<!-- date: 2025-03-09 -->
<!-- title: Lemma for FTGT -->
<!-- tag: Mathematics -->
<!-- key: udjib -->
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<h2 id="introduction">Introduction</h2>
<p>
  This post illustrates a key lemma that is used in proving
  the <em>fundamental theorem of Galois theory</em> (FTGT).  Note that
  FTGT is not covered in this post.  The focus of this post is on
  understanding and proving this lemma only.  Here is the lemma from
  the book <em>Galois Theory</em>, 5th ed. by Stewart (2023):
</p>
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