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 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).