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Intermediate notions between [[normal subgroup]] and [[conjugacy-closed normal subgroup]] | Intermediate notions between [[normal subgroup]] and [[conjugacy-closed normal subgroup]]# |
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Normal subgroup whose center is contained in the center of the whole group | Normal subgroup whose center is contained in the center of the whole group |

Normal subgroup whose focal subgroup equals its derived subgroup | Normal subgroup whose focal subgroup equals its derived subgroup |

Transitively normal subgroup | Transitively normal subgroup |