Let $G$ be a group and let $K$ be a normal subgroup of $G.$ Now let $H$ and $N$ be normal subgroups of $G$ containing $K.$ Given $N/K=H/K$ can I show $N=H$ necessarily? Is there a way?
2026-04-01 12:55:17.1775048117
Does N/H=K/H under some terms mean N=K?
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If $H/K = N/K$, then $N=H$ by the correspondence theorem: there is a bijection between the subgroups of $G$ containing $K$ and the subgroups of $G/K$