Analytic pro-p groups of small dimensions
| dc.creator | González-Sánchez, Jon | |
| dc.creator | Klopsch, Benjamin | |
| dc.date | 2008-06-18 | |
| dc.date.accessioned | 2026-07-07T09:45:21Z | |
| dc.date.available | 2026-07-07T09:45:21Z | |
| dc.description | According to Lazard, every p-adic Lie group contains an open pro-p subgroup which is saturable. This can be regarded as the starting point of p-adic Lie theory, as one can naturally associate to every saturable pro-p group G a Lie lattice L(G) over the p-adic integers. Essential features of saturable pro-p groups include that they are torsion-free and p-adic analytic. In the present paper we prove a converse result in small dimensions: every torsion-free p-adic analytic pro-p group of dimension less than p is saturable. This leads to useful consequences and interesting questions. For instance, we give an effective classification of 3-dimensional soluble torsion-free p-adic analytic pro-p groups for p > 3. Our approach via Lie theory is comparable with the use of Lazard's correspondence in the classification of finite p-groups of small order. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0806.2968 | |
| dc.identifier | http://arxiv.org/abs/0806.2968 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163164 | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 20E18 (Primary) 22E20, 20F05 (Secondary) | |
| dc.title | Analytic pro-p groups of small dimensions | |
| dc.type | text |