# Direct product-closed subgroup property

From Groupprops

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property

View a complete list of subgroup metaproperties

View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

## Contents |

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

This article is about a general term. A list of important particular cases (instances) is available at Category:Direct product-closed subgroup properties

## Definition

### Definition with symbols

A subgroup property is termed **direct product-closed** if, given a nonempty indexing set , and a collection of group-subgroup pairs for , such that each satisfies as a subgroup of , then the direct product of the s satisfies via its natural embedding in the direct product of s.