×

Finitely presented simple groups and products of trees. (English. Abridged French version) Zbl 0966.20013

From the introduction: We construct an infinite family of torsion-free finitely presented simple groups. For every pair \((n,m)\) of sufficiently large even integers, we construct a finite square complex \({\mathcal Y}_{n,m}\) whose universal covering is the product \(T_n\times T_m\) of regular trees of respective degrees \(n\) and \(m\) and whose fundamental group \(\Gamma_{n,m}\) enjoys the following properties: Theorem: (1) The group \(\Gamma_{n,m}\) is simple, finitely presented and isomorphic to a free amalgam \(F*_GF\) where \(F\), \(G\) are finitely generated free groups. (2) If \(\Gamma_{n,m}\) is isomorphic to \(\Gamma_{k,l}\), then the corresponding complexes \({\mathcal Y}_{n,m}\) and \({\mathcal Y}_{k,l}\) are isomorphic, and \(\{n,m\}=\{k,l\}\).

MSC:

20E08 Groups acting on trees
20E32 Simple groups
20F05 Generators, relations, and presentations of groups
PDFBibTeX XMLCite
Full Text: DOI