Lower central series condition

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 metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

Definition

A subgroup property $p$ is said to satisfy the lower central series condition if, whenever $H\leq G$ is a subgroup satisfying property $p$, we have that $\gamma _{k}(H)$ satisfies property $p$ in $\gamma _{k}(G)$ for all positive integers $k$.

Formalisms

This article defines a single-input-expressible subgroup metaproperty