Relatively free nilpotent torsion-free groups and their Lie algebras
| dc.creator | Kofinas, C. | |
| dc.creator | Metaftsis, V. | |
| dc.creator | Papistas, A. I. | |
| dc.date | 2009-03-09 | |
| dc.date.accessioned | 2026-07-07T12:50:30Z | |
| dc.date.available | 2026-07-07T12:50:30Z | |
| dc.description | For a torsion free finitely generated nilpotent group G we naturally associate four finite dimensional nilpotent Lie algebras over a field of characteristic zero. We show that if G is a relatively free group of some variery of nilpotent groups then all the above Lie algebras are isomorphic. As a result, any two quasi-isometric relatively free nilpotent groups are isomorphic. Moreover let L be a relatively free nilpotent Lie algebra over Q generated by X. We give L the structure of a group by means of the Baker-Campbell-Hausdorff formula and we show that the subgroup H generated by X is relatively free in some variety of nilpotent groups, is Magnus and certain Lie algebras associated to H are isomorphic. This isomorphism is extended to relatively free residually torsion-free nilpotent groups. Finally, we give an example that demonstrates that this is not always the case with finitely generated Magnus nilpotent groups. | |
| dc.description | 49 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0903.1573 | |
| dc.identifier | http://arxiv.org/abs/0903.1573 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222705 | |
| dc.subject | Group Theory | |
| dc.subject | 20F40 | |
| dc.title | Relatively free nilpotent torsion-free groups and their Lie algebras | |
| dc.type | text |