2009/03/09 by C. Kofinas, C. E. Kofinas, V. Metaftsis +4
Mathematics · #20F40 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20F40
paper · pdf · doi:10.48550/arxiv.0903.1573
49 pages, no figures
arxiv created 2009/03/09 · openalex publication_date 2009/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.