The examples I've seen so far are not undergraduate-level, at least, not anywhere I've taught. The Fundamental Theorem of Galois Theory is undergraduate-level, and can be stated, in part, as follows: let if $K$ be is separable (that's one), normal (that's two), and finite (that's three!) over $F$, then the number of elements in the Galois group of $K$ over $F$ equals the degree of $K$ over $F$.
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The examples I've seen so far are not undergraduate-level, at least, not anywhere I've taught. The Fundamental Theorem of Galois Theory is undergraduate-level, and can be stated, in part, as follows: let $K$ be separable (that's one), normal (that's two), and finite (that's three!) over $F$, then the number of elements in the Galois group of $K$ over $F$ equals the degree of $K$ over $F$. |
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