Commutator-realizable group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

A group is termed commutator-realizable if it can be realized as the commutator subgroup of some group.

Relation with other properties

Stronger properties

Facts

Metaproperties

Characteristic quotients

This group property is characteristic quotient-closed: the quotient group by any characteristic subgroup, of a group with this property, also has this property
View other characteristic quotient-closed group properties

If G is commutator-realizable, and H is a characteristic subgroup of G, G/H is also a commutator-realizable group.