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Counterexample

Is this true?

G/Z(G) can be cyclic and non-trivial

No — it is false.

The counterexample

Impossible — if G/Z is cyclic then G is abelian, so G/Z is trivial

Why it fails

This 'no counterexample exists' fact is itself examined: |G/Z| is never prime.

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Execution slip

The idea was right. The computation was not.

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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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