Stallings theorem about ends of groups
GPTKB entity
Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
ends of groups
|
| gptkbp:field |
group theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Stallings theorem about ends of groups
|
| gptkbp:implies |
A finitely generated infinite group has 1, 2, or infinitely many ends.
|
| gptkbp:namedAfter |
gptkb:John_R._Stallings
|
| gptkbp:publishedIn |
gptkb:Annals_of_Mathematics
|
| gptkbp:relatedTo |
gptkb:Bass–Serre_theory
gptkb:Serre's_theorem_on_trees accessibility of groups |
| gptkbp:state |
A finitely generated group has more than one end if and only if it splits as a nontrivial amalgamated free product or HNN extension over a finite subgroup.
|
| gptkbp:usedIn |
geometric group theory
|
| gptkbp:yearProved |
1971
|
| gptkbp:bfsParent |
gptkb:John_R._Stallings
|
| gptkbp:bfsLayer |
7
|