# Normal subgroup satisfying the subgroup-to-quotient powering-invariance implication

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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

Suppose is a normal subgroup of a group . We say that satisfies a **subgroup-to-quotient powering-invariance implication** if for any prime such that both and are powered over , the quotient group is also powered over .