# Relative-intersection-closed subgroup property

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 property is termed **relative-intersection-closed** if it satisfies the following:

Suppose is a well-ordered set. Suppose is a collection of subgroups of a group , such that for any , satisfies property in some subgroup of containing both and . Then:

satisfies property in .