Normal subgroup whose derived subgroup equals its intersection with whole derived subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and subgroup whose commutator subgroup equals its intersection with whole commutator subgroup
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Definition

A subgroup H of a group G is termed a normal subgroup whose commutator subgroup equals its intersection with whole commutator subgroup if it satisfies the following equivalent conditions:

  1. H is a normal subgroup of G and [H,H] = H \cap [G,G].
  2. [H,H] = [G,H] = H \cap [G,G].

Relation with other properties

Stronger properties

Weaker properties