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Is this true?

A group of order pq (p < q) is always cyclic

No — it is false.

The counterexample

of order 6 = 2·3

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

The kind of mistake this is

Execution slip

The idea was right. The computation was not.

Drill statements like this
groupssylow

Others that fail the same way

From Groups › Sylow theorems and groups of small order

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