Quotient-isomorph-free subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties [SHOW MORE]
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Definition

A subgroup $H$ of a group $G$ is termed quotient-isomorph-free if $H$ is normal in $G$ , and there is no other normal subgroup $K$ of $G$ such that $G/H$ is isomorphic to $G/K$ .