Pro‐p groups of positive deficiency
Let Γ be a finitely presentable pro?p group with a nontrivial, finitely generated closed normal subgroup N of infinite index. Then def (Γ) ? 1, and if def (Γ) = 1 then Γ is a pro?p duality group of dimension 2, N is a free pro?p group and Γ/N is virtually free. In particular, if the centre of Γ is n...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
3 October 2008
|
| In: |
Bulletin of the London Mathematical Society
Year: 2008, Jahrgang: 40, Heft: 6, Pages: 1065-1069 |
| ISSN: | 1469-2120 |
| DOI: | 10.1112/blms/bdn089 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1112/blms/bdn089 Verlag, Volltext: https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms/bdn089 
|
| Verfasserangaben: | Jonathan A. Hillman and Alexander Schmidt |
| Zusammenfassung: | Let Γ be a finitely presentable pro?p group with a nontrivial, finitely generated closed normal subgroup N of infinite index. Then def (Γ) ? 1, and if def (Γ) = 1 then Γ is a pro?p duality group of dimension 2, N is a free pro?p group and Γ/N is virtually free. In particular, if the centre of Γ is nontrivial and def (Γ) ? 1, then def (Γ) = 1, cd G ? 2 and Γ is virtually a direct product F ? ?p, with F a finitely generated free pro?p group. |
|---|---|
| Beschreibung: | Gesehen am 04.05.2018 |
| Beschreibung: | Online Resource |
| ISSN: | 1469-2120 |
| DOI: | 10.1112/blms/bdn089 |