# Normal subgroup whose focal subgroup equals its 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 focal subgroup equals its commutator subgroup

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## Definition

A **normal subgroup whose focal subgroup equals its commutator subgroup** is a subgroup of a group satisfying the following equivalent conditions:

- is a normal subgroup of and , i.e., is a subgroup whose focal subgroup equals its commutator subgroup.
- .