# Intersection-transitively permutable subgroup

From Groupprops

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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 of a group is termed **intersection-transitively permutable** if its intersection with any permutable subgroup of the group is again permutable in the whole group.

Note that permutability is not finite-intersection-closed.

## Formalisms

### In terms of the intersection-transiter

This property is obtained by applying the intersection-transiter to the property: permutable subgroup

View other properties obtained by applying the intersection-transiter