# Join of finitely many direct factors

From Groupprops

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]

## Contents

## Definition

A subgroup of a group is termed a **join of finitely many direct factors** if it can be expressed as the join of finitely many subgroups, each of which is a direct factor of the whole group.

## Relation with other properties

### Stronger properties

- Direct factor: The
*strictness*follows from the fact that direct factor is not finite-join-closed.