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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

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

The kind of mistake this is

Execution slip

The idea was right. The computation was not.

Drill statements like this
groups

Others that fail the same way

From Groups › Group actions, class equation, p-groups

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