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Elementary amenable group

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.

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Mathematics Group Finite groups Abelian groups Amenable groups

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Overview

Mathematics
Group Group (mathematics)
Finite groups Finite group
Abelian groups Abelian group
Amenable groups Amenable group
Subgroups Subgroup
Quotients Quotient group
Extensions Group extension
Directed unions Directed union
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Elementary amenable group

Nodes12

Edges11

Triples11

Avg. degree1.83

Density0.166667

Components1

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Elementary amenable group

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related to References · 11

Elementary amenable group → Ching, Chou, Elementary, Illinois Journal, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Mathematics, MR, S2CID, Wikisource-logo

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elementary amenable groups group finite abelian operations mathematics subgroups quotients extensions called built sequence simple result applied since every however

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Subject	Predicate	Object	Confidence	Src
Elementary amenable group	related to References	Lock-green	0.60	section
Elementary amenable group	related to References	Lock-gray-alt-2	0.60	section
Elementary amenable group	related to References	Lock-red-alt-2	0.60	section
Elementary amenable group	related to References	Wikisource-logo	0.60	section
Elementary amenable group	related to References	Chou	0.60	section
Elementary amenable group	related to References	Ching	0.60	section
Elementary amenable group	related to References	Elementary	0.60	section
Elementary amenable group	related to References	Illinois Journal	0.60	section
Elementary amenable group	related to References	Mathematics	0.60	section
Elementary amenable group	related to References	MR	0.60	section
Elementary amenable group	related to References	S2CID	0.60	section

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