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The query [[Defining ingredient::Abelian group]] was answered by the SMWSQLStore3 in 0.0049 seconds.


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 Quick phraseDefining ingredient
2-Engel groupNormal 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 subgroupSylow subgroup
Abelian group
Abelian characteristic subgroupCharacteristic subgroup
Abelian group
Abelian conjugacy-closed subgroupConjugacy-closed subgroup
Abelian group
Abelian critical subgroupCritical subgroup
Abelian group
Abelian direct factorDirect factor
Abelian group
Central subgroup
Abelian fully invariant subgroupFully invariant subgroup
Abelian group
Abelian hereditarily normal subgroupHereditarily normal subgroup
Abelian group
Transitively normal subgroup
Abelian normal subgroup
Abelian marginal subgroupMarginal subgroup
Abelian group
Abelian normal subgroupNormal subgroup
Abelian group
Abelian normal subgroup of maximum rankAbelian normal subgroup
Abelian group
Normal subgroup
Rank of a p-group
Normal rank of a p-group
Abelian pronormal subgroupPronormal subgroup
Abelian group
Abelian subgroupAbelian group
Abelian subnormal subgroupSubnormal subgroup
Abelian group
Abelian verbal subgroupVerbal subgroup
Abelian group
Associative ringAbelian group
CA-groupCentralizer
Abelian group
Centerless group
Center
Central subgroupCentral factor
Abelian group
Central subgroup of normalizerCentral factor of normalizer
Abelian group
Central subgroup
Center
In-normalizer operator
Characteristic direct factor of abelian groupCharacteristic direct factor
Abelian group
Fully invariant direct factor
Characteristic subgroup of abelian groupCharacteristic subgroup
Abelian group
Constant APS of an abelian groupAbelian group
Divisibility-closed subgroup of abelian groupDivisibility-closed subgroup
Abelian group
Division ringAbelian group
Associative binary operation
FieldAbelian group
Finite group that is order statistics-equivalent to an abelian groupOrder statistics-equivalent finite groups
Order statistics of a finite group
Abelian group
Finite abelian group
Fully invariant subgroup of abelian groupFully invariant subgroup
Abelian group
Group admitting a partition into abelian subgroupsAbelian subgroup
Abelian group
Group having an abelian contranormal subgroupAbelian group
Contranormal subgroup
Normal closure
Group of nilpotency class twoclass 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 group1-isomorphic groups
Abelian group
Group whose automorphism group is abelianabelian 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 factorCenterless group
Abelian group
Center
Permutably complemented subgroup
Complemented normal subgroup
Direct factor
Lie ring of nilpotency class twoclass 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 subgroupsSelf-centralizing subgroup
Abelian group
Maximal operator
Abelian subgroup
Metabelian groupabelian-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 ringAbelian group
Powering-invariant subgroup of abelian groupPowering-invariant subgroup
Abelian group
Residually finite abelian groupResidually finite group
Abelian group
Conjugacy-separable group
Solvable groupNormal series
Abelian group
Subnormal series
Derived series
Derived subgroup
Characteristic series
Fully invariant series
Subgroup of abelian groupSubgroup
Abelian group
Verbal subgroup of abelian groupVerbal subgroup
Abelian group
Virtually abelian groupVirtually operator
Abelian group