# Intermediately local powering-invariant 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]

## Definition

A subgroup $H$ of a group $G$ is termed intermediately local powering-invariant in $G$ if, for every intermediate subgroup $K$ of $G$ (i.e., $H \le K \le G$), $H$ is a local powering-invariant subgroup of $K$.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
intermediately powering-invariant subgroup powering-invariant in every intermediate subgroup. |FULL LIST, MORE INFO