# Lower central series condition

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

## Definition

A subgroup property is said to satisfy the **lower central series** condition if, whenever is a subgroup satisfying property , we have that satisfies property in for all positive integers .

## Formalisms

This article defines a single-input-expressible subgroup metaproperty