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 metaproperty
VIEW 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