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May 6, 2019 at 14:00 comment added André Macedo Many thanks, Derek Holt! A quick observation: in the case where $K \subset [\overline{H},\overline{G}]$ (this happens for instance when $\operatorname{Cor}:\operatorname{H}_2(H,\mathbb{Z}) \to \operatorname{H}_2(G,\mathbb{Z})$ is surjective) the resulting quotient is also isomorphic to $\frac{H \cap [G,G]}{[H,G]}$.
May 6, 2019 at 12:02 vote accept André Macedo
May 3, 2019 at 20:54 history edited Derek Holt CC BY-SA 4.0
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May 3, 2019 at 18:57 history edited Derek Holt CC BY-SA 4.0
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May 3, 2019 at 18:41 history answered Derek Holt CC BY-SA 4.0