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
This is a variation of solvability|Find other variations of solvability |
This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
VIEW: Definitions built on this | Facts about this: (facts closely related to Hyperabelian group, all facts related to Hyperabelian group) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a list of other standard non-basic definitions
A hyperabelian group is a group which possesses an ascending (possibly transfinite) normal series where all the successive quotients are Abelian.
Relation with other properties
This group property is subgroup-closed, viz., any subgroup of a group satisfying the property also satisfies the property
View a complete list of subgroup-closed group properties
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.[SHOW MORE]