# Upper join of characteristic subgroups

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 characteristic subgroups** if there exist subgroups of containing (where is an indexing set) such that:

- is a characteristic subgroup inside .
- The join of the s is .

Note that need not be a characteristic subgroup of because characteristicity is not upper join-closed.

## Formalisms

### In terms of the upper join-closure operator

This property is obtained by applying the upper join-closure operator to the property: characteristic subgroup

View other properties obtained by applying the upper join-closure operator