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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Complex Analysis, Algebra & Topology › Rings and Fields

“Every extension of degree n has a Galois group of order n” — false

Counterexample: ℚ(∛2)/ℚ has degree 3 but only the identity automorphism

The extension is not normal — the other cube roots are not real. Order = degree only for Galois extensions.

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