Can anyone help me in this question :-

**Prove or disprove**: If \(H\) is a normal subgroup of \(G\) such that \(H\) and \(G/H\) are
abelian, then \(G\) is abelian.

I don't need any counter example. I need a proper proof.

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## Comments

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TopNewestWell, it turns out that giving a counter example is a

proper proof.Taking \(G=S_3\) and \(H=A_3\) we see that the hypothesis is satisfied though \(G\) isn't abelian.

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@Kushal Bose

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Unfortunately, false statements cannot be proven in a consistent system.

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Of course they can be!

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But I suppose there are statements which cannot be proven or disproven.

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@Deeparaj Bhat Check this out

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