Commutator of a normal subgroup and a subset

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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 commutator of a normal subgroup and a subset if there exists a normal subgroup N of G and a subset S of G such that H is the commutator [N,S], i.e., the subgroup generated by all the commutators between elements of N and elements of S.

Relation with other properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
commutator of a transitively normal subgroup and a subset

Stronger properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
2-subnormal subgroup normal subgroup of normal subgroup commutator of a normal subgroup and a subset implies 2-subnormal |FULL LIST, MORE INFO