In mathematics, a group is called elementary amenable if it can be built up from finite groups and abelian groups by a sequence of simple operations that result in amenable groups when applied to amenable groups.
Since finite groups and abelian groups are amenable, every elementary amenable group is amenable - however, the converse is not true.
Formally, the class of elementary amenable groups is the smallest subclass of the class of all groups that satisfies the following conditions: The Tits alternative implies that any amenable linear group is locally virtually solvable; hence, for linear groups, amenability and elementary amenability coincide.
This group theory-related article is a stub.
You can help Wikipedia by expanding it.