# Upper join of direct factors

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 an **upper join of direct factors** if there exist intermediate subgroups of containing , such that:

- The join of the s is equal to .
- is a direct factor in each of the s.