Counterexample

Is this true?

Every group of order $p^{2}$ is cyclic

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Execution slip

The idea was right. The computation was not.

See real exam options built on this mistake Drill statements like this

groups p-groups

Go deeper· Explained in full in Group actions, the class equation and p-groups· Asked in CSIR NET December 2025· From Groups › Group actions, class equation, p-groups

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