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- Elementary_amenable_group abstract "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:it contains all finite and all abelian groupsif G is in the subclass and H is isomorphic to G, then H is in the subclassit is closed under the operations of taking subgroups, forming quotients, and forming extensionsit is closed under directed unions.The Tits alternative implies that any amenable linear group is locally virtually solvable; hence, for linear groups, amenability and elementary amenability coincide.".
- Elementary_amenable_group wikiPageID "5393997".
- Elementary_amenable_group wikiPageLength "1220".
- Elementary_amenable_group wikiPageOutDegree "12".
- Elementary_amenable_group wikiPageRevisionID "634854058".
- Elementary_amenable_group wikiPageWikiLink Abelian_group.
- Elementary_amenable_group wikiPageWikiLink Amenable_group.
- Elementary_amenable_group wikiPageWikiLink Category:Infinite_group_theory.
- Elementary_amenable_group wikiPageWikiLink Category:Properties_of_groups.
- Elementary_amenable_group wikiPageWikiLink Direct_limit.
- Elementary_amenable_group wikiPageWikiLink Finite_group.
- Elementary_amenable_group wikiPageWikiLink Group_(mathematics).
- Elementary_amenable_group wikiPageWikiLink Group_extension.
- Elementary_amenable_group wikiPageWikiLink Mathematics.
- Elementary_amenable_group wikiPageWikiLink Quotient_group.
- Elementary_amenable_group wikiPageWikiLink Subgroup.
- Elementary_amenable_group wikiPageWikiLink Tits_alternative.
- Elementary_amenable_group wikiPageWikiLinkText "Elementary amenable group".
- Elementary_amenable_group wikiPageWikiLinkText "elementary amenable group".
- Elementary_amenable_group wikiPageWikiLinkText "elementary amenable".
- Elementary_amenable_group wikiPageUsesTemplate Template:Algebra-stub.
- Elementary_amenable_group subject Category:Infinite_group_theory.
- Elementary_amenable_group subject Category:Properties_of_groups.
- Elementary_amenable_group comment "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.".
- Elementary_amenable_group label "Elementary amenable group".
- Elementary_amenable_group sameAs Q5358894.
- Elementary_amenable_group sameAs m.0djwbc.
- Elementary_amenable_group sameAs Q5358894.
- Elementary_amenable_group wasDerivedFrom Elementary_amenable_group?oldid=634854058.
- Elementary_amenable_group isPrimaryTopicOf Elementary_amenable_group.