Group in which every element is a commutator
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 non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Note that this property does not depend on whether we use the left or right convention for commutators.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Perfect group||The commutators form a generating set||(obvious)||perfect not implies every element is a commutator|||FULL LIST, MORE INFO|