This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications  Group property nonimplications Group metaproperty satisfactions  Group metaproperty dissatisfactions  Group property satisfactions  Group property dissatisfactions
Definition
A group is termed group whose derived subgroup is contained in the square of its center if it satisfies the following equivalent conditions:
 For every , there exists in the center such that , where denotes the commutator of and .
 The derived subgroup is contained in the subgroup where is the center of .
Relation with other properties
Stronger properties
Property 
Meaning 
Proof of implication 
Proof of strictness (reverse implication failure) 
Intermediate notions

abelian group 



CSBaer Lie group, Group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycle, Group of nilpotency class two whose commutator map is the double of an alternating bihomomorphism giving class two, LCSBaer Lie groupFULL LIST, MORE INFO

Baer Lie group 



CSBaer Lie group, Group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycle, Group of nilpotency class two whose commutator map is the double of an alternating bihomomorphism giving class two, LCSBaer Lie group, LUCSBaer Lie group, UCSBaer Lie groupFULL LIST, MORE INFO

LCSBaer Lie group 



CSBaer Lie group, Group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycle, Group of nilpotency class two whose commutator map is the double of an alternating bihomomorphism giving class twoFULL LIST, MORE INFO

UCSBaer Lie group 



CSBaer Lie group, Group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycle, LUCSBaer Lie groupFULL LIST, MORE INFO

LUCSBaer Lie group 



CSBaer Lie group, Group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycleFULL LIST, MORE INFO

CSBaer Lie group 



Group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycle, Group of nilpotency class two whose commutator map is the double of an alternating bihomomorphism giving class twoFULL LIST, MORE INFO

group of nilpotency class two whose commutator map is the double of an alternating bihomomorphism giving class two 



Group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycleFULL LIST, MORE INFO

group of nilpotency class two whose commutator map is the double of a skewsymmetric cyclicitypreserving 2cocycle 



FULL LIST, MORE INFO

Weaker properties