2-Engel group | | Normal closure Normal subgroup generated by a subset Abelian group Abelian normal subgroup Local nilpotency class Group of nilpotency class two Bounded Engel group Levi operator |

Abelian Sylow subgroup | | Sylow subgroup Abelian group |

Abelian characteristic subgroup | | Characteristic subgroup Abelian group |

Abelian conjugacy-closed subgroup | | Conjugacy-closed subgroup Abelian group |

Abelian critical subgroup | | Critical subgroup Abelian group |

Abelian direct factor | | Direct factor Abelian group Central subgroup |

Abelian fully invariant subgroup | | Fully invariant subgroup Abelian group |

Abelian hereditarily normal subgroup | | Hereditarily normal subgroup Abelian group Transitively normal subgroup Abelian normal subgroup |

Abelian marginal subgroup | | Marginal subgroup Abelian group |

Abelian normal subgroup | | Normal subgroup Abelian group |

Abelian normal subgroup of maximum rank | | Abelian normal subgroup Abelian group Normal subgroup Rank of a p-group Normal rank of a p-group |

Abelian pronormal subgroup | | Pronormal subgroup Abelian group |

Abelian subgroup | | Abelian group |

Abelian subnormal subgroup | | Subnormal subgroup Abelian group |

Abelian verbal subgroup | | Verbal subgroup Abelian group |

Associative ring | | Abelian group |

CA-group | | Centralizer Abelian group Centerless group Center |

Central subgroup | | Central factor Abelian group |

Central subgroup of normalizer | | Central factor of normalizer Abelian group Central subgroup Center In-normalizer operator |

Characteristic direct factor of abelian group | | Characteristic direct factor Abelian group Fully invariant direct factor |

Characteristic subgroup of abelian group | | Characteristic subgroup Abelian group |

Constant APS of an abelian group | | Abelian group |

Divisibility-closed subgroup of abelian group | | Divisibility-closed subgroup Abelian group |

Division ring | | Abelian group Associative binary operation |

Field | | Abelian group |

Finite group that is order statistics-equivalent to an abelian group | | Order statistics-equivalent finite groups Order statistics of a finite group Abelian group Finite abelian group |

Fully invariant subgroup of abelian group | | Fully invariant subgroup Abelian group |

Group admitting a partition into abelian subgroups | | Abelian subgroup Abelian group |

Group having an abelian contranormal subgroup | | Abelian group Contranormal subgroup Normal closure |

Group of nilpotency class two | class two inner automorphism group is abelian commutator subgroup inside center derived subgroup inside center commutators are central triple commutators are trivial | Nilpotency class Derived subgroup Center Inner automorphism group Abelian group |

Group that is 1-isomorphic to an abelian group | | 1-isomorphic groups Abelian group |

Group whose automorphism group is abelian | abelian automorphism group any two automorphisms commute | Automorphism group of a group Abelian group Normal subgroup Normal subgroup contained in centralizer of derived subgroup |

Group whose center is a direct factor | | Centerless group Abelian group Center Permutably complemented subgroup Complemented normal subgroup Direct factor |

Lie ring of nilpotency class two | class two inner derivation Lie ring is abelian derived subring inside center Lie brackets are central triple Lie brackets are trivial | Nilpotency class Derived subring of a Lie ring Center Inner derivation Abelian group |

Maximal among abelian subgroups | | Self-centralizing subgroup Abelian group Maximal operator Abelian subgroup |

Metabelian group | abelian-by-abelian abelian normal subgroup with abelian quotient abelian derived subgroup abelian commutator subgroup | Solvable group Derived length Derived subgroup Abelian group Abelian normal subgroup Abelian-quotient subgroup Commutator Meta operator |

Non-associative ring | | Abelian group |

Powering-invariant subgroup of abelian group | | Powering-invariant subgroup Abelian group |

Residually finite abelian group | | Residually finite group Abelian group Conjugacy-separable group |

Solvable group | | Normal series Abelian group Subnormal series Derived series Derived subgroup Characteristic series Fully invariant series |

Subgroup of abelian group | | Subgroup Abelian group |

Verbal subgroup of abelian group | | Verbal subgroup Abelian group |

Virtually abelian group | | Virtually operator Abelian group |