| 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 |
