Hyperabelian group

Symbol-free definition
A hyperabelian group is a group which possesses an ascending (possibly transfinite) normal series where all the successive quotients are Abelian.

Stronger properties

 * Solvable group
 * Hypercentral group

Weaker properties

 * Locally solvable group

Metaproperties
The ascending normal series for the subgroup is simply the intersection with the subgroup of the ascending normal series for the whole group.

The ascending normal series for the quotient is the image of the ascending normal series for the whole group via the quotient map.