Elementary amenable group

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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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

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

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).

Relation with other properties

Stronger properties

Weaker properties