Elementary amenable group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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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 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).