Lower central series condition

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

A subgroup property $p$ is said to satisfy the lower central series condition if, whenever $H \le G$ 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