I'm probably missing something obvious, but suppose that B' < B < A are all abelian groups and that A/B is isomorphic to A/B'. Does it follow that B = B'? In the case of finite groups and vector spaces it is true by counting orders and dimensions but what about in general?(adsbygoogle = window.adsbygoogle || []).push({});

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# Does A/B' = A/B imply B' = B?

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