Elementary amenable group

Definition
A group is said to be elementary amenable if it can be built from finite groups and Abelian groups by the following operations:


 * Taking subgroups
 * Taking quotient groups
 * Taking group extensions
 * Taking directed unions

Since each of these operations preserves amenability, every elementary amenable group is an amenable discrete group (viz, its amenable when viewed with the discrete topology).

Stronger properties

 * Finite group
 * Abelian group
 * Solvable group

Weaker properties

 * Amenable discrete group