About: Stallings theorem about ends of groups

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In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or an HNN extension over a finite subgroup. In the modern language of Bass–Serre theory the theorem says that a finitely generated group G has more than one end if and only if G admits a nontrivial (that is, without a global fixed point) action on a simplicial tree with finite edge-stabilizers and without edge-inversions.

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rdf:type	yago:WikicatTheoremsInGroupTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Satz von Stallings (de) Théorème de Stallings (fr) Stallings theorem about ends of groups (en)
rdfs:comment	Der Satz von Stallings ist ein Lehrsatz aus dem mathematischen Gebiet der Gruppentheorie, der Gruppen mit mehr als einem Ende charakterisiert. Aus ihm ergibt sich die gelegentlich ebenfalls als Satz von Stallings oder Satz von Stallings-Swan bezeichnete Charakterisierung freier Gruppen durch ihre kohomologische Dimension. John Stallings und Richard Swan erhielten dafür den Colepreis für Algebra. (de) Le théorème de Stallings est un théorème de la théorie des groupes des groupes qui caractérise les groupes à plusieurs bouts. Il en résulte une caractérisation des groupes libres par leur dimension cohomologique, parfois aussi appelée théorème de Stallings ou théorème de Stallings-Swan. John Stallings et Richard Swan ont reçu le prix Frank-Nelson-Cole d'algèbre pour ces résultats. (fr) In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or an HNN extension over a finite subgroup. In the modern language of Bass–Serre theory the theorem says that a finitely generated group G has more than one end if and only if G admits a nontrivial (that is, without a global fixed point) action on a simplicial tree with finite edge-stabilizers and without edge-inversions. (en)
dcterms:subject	Geometric group theory Theorems in group theory
Wikipage page ID	19196631 (xsd:integer)
Wikipage revision ID	1034093708 (xsd:integer)
Link from a Wikipage to another Wikipage	End (graph theory) End (topology) CAT(0) space Topological dimension John R. Stallings Index of a subgroup Quasi-isometry Geometric group theory Geometric group theory Free product with amalgamation Generating set of a group Graph (discrete mathematics) Graph of groups Martin Dunwoody Bass–Serre theory Polycyclic group Subgroup C. T. C. Wall Theorems in group theory Tree (graph theory) HNN extension Minimal surface Brian Bowditch Cayley graph Hans Freudenthal Riemannian geometry Group action (mathematics) Heinz Hopf Torsion-free group Virtually Free abelian group Free group Free product Connected component (graph theory) Group theory HNN-extension Terry Wall Infinite cyclic group Infinite dihedral group Mladen Bestvina Symmetric difference Finitely generated group Finitely presented group Topological space Word-hyperbolic group Cell complex Mikhail Gromov (mathematician)
sameAs	Stallings theorem about ends of groups Stallings theorem about ends of groups Stallings theorem about ends of groups Stallings theorem about ends of groups Stallings theorem about ends of groups Stallings theorem about ends of groups
dbp:wikiPageUsesTemplate	dbt:Main dbt:Reflist
has abstract	Der Satz von Stallings ist ein Lehrsatz aus dem mathematischen Gebiet der Gruppentheorie, der Gruppen mit mehr als einem Ende charakterisiert. Aus ihm ergibt sich die gelegentlich ebenfalls als Satz von Stallings oder Satz von Stallings-Swan bezeichnete Charakterisierung freier Gruppen durch ihre kohomologische Dimension. John Stallings und Richard Swan erhielten dafür den Colepreis für Algebra. (de) In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or an HNN extension over a finite subgroup. In the modern language of Bass–Serre theory the theorem says that a finitely generated group G has more than one end if and only if G admits a nontrivial (that is, without a global fixed point) action on a simplicial tree with finite edge-stabilizers and without edge-inversions. The theorem was proved by John R. Stallings, first in the torsion-free case (1968) and then in the general case (1971). (en) Le théorème de Stallings est un théorème de la théorie des groupes des groupes qui caractérise les groupes à plusieurs bouts. Il en résulte une caractérisation des groupes libres par leur dimension cohomologique, parfois aussi appelée théorème de Stallings ou théorème de Stallings-Swan. John Stallings et Richard Swan ont reçu le prix Frank-Nelson-Cole d'algèbre pour ces résultats. (fr)
prov:wasDerivedFrom	wikipedia-en:Stallings_theorem_about_ends_of_groups?oldid=1034093708&ns=0
page length (characters) of wiki page	21851 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stallings_theorem_about_ends_of_groups
is Link from a Wikipage to another Wikipage of	End (graph theory) End (topology) John R. Stallings Quasi-isometry Geometric group theory Martin Dunwoody Stalling C. T. C. Wall Brian Bowditch Heinz Hopf Eilenberg–Ganea theorem Virtually List of theorems Muller–Schupp theorem Wall's conjecture
is Wikipage disambiguates of	Stalling
is known for of	Heinz Hopf
is known for of	John R. Stallings Heinz Hopf
is foaf:primaryTopic of	wikipedia-en:Stallings_theorem_about_ends_of_groups

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