LCS-powering-invariant subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup] H of a group G is termed LCS-powering-invariant if for every positive integer k, the k^{th} member \gamma_k(H) of the lower central series of H is a powering-invariant subgroup inside the k^{th} member \gamma_k(G) of the lower central series of G.

Facts

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite subgroup |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
powering-invariant subgroup |FULL LIST, MORE INFO