LCS-characteristic 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 a LCS-characteristic subgroup if, for every positive integer k, the subgroup \gamma_k(H) (defined as the k^{th} member of the lower central series of H) is a characteristic subgroup inside \gamma_k(G) (defined as the k^{th} member of the lower central series of G).

Relation with other properties

Stronger properties

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

Weaker properties

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