Hypoabelian group

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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This is a variation of solvability|Find other variations of solvability |

This is an opposite of perfectness

Definition

Symbol-free definition

A group is termed hypoAbelian if the following equivalent conditions are satisfied:

• The perfect core is trivial
• The hypoAbelianization is the whole group
• The derived series terminates at the identity
• There is no nontrivial perfect subgroup.
• There is a descending strongly normal series where all the successive quotients are Abelian

Relation with other properties

Stronger properties

• Solvable group
• Hypocentral group

Weaker properties

• Locally solvable group