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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 › Groups

“A group of order pq (p < q) is always cyclic” — false

Counterexample: S₃ of order 6 = 2·3

Non-abelian because 2 | 3 − 1. The cyclic conclusion needs p ∤ q − 1.

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