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Counterexample

Is this true?

H ⊴ K and K ⊴ G ⇒ H ⊴ G

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.

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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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