Elementary amenable group

Summary

The elementary amenable groups are the groups that can be built from finite groups and abelian groups by taking subgroups, quotients, extensions and directed unions. Each of these operations preserves amenability, so every elementary amenable group is amenable. The class contains all solvable groups and all virtually solvable groups. There are amenable groups that are not elementary amenable, such as the Grigorchuk group, so the class is strictly smaller.