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Counterexample

Is this true?

If every subgroup of G is normal then G is abelian

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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

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Property not inherited

A property assumed to pass to subobjects, quotients, or through a chain. It does not.

See real exam options built on this mistakeDrill statements like this
groups

Go deeper· Explained in full in Normal subgroups, quotients and the isomorphism theorems· Asked in CSIR NET June 2025· From Groups › Normal subgroups, quotients, isomorphism theorems

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