Groups of cohomological codimension one
[Groupes de codimension cohomologique un]
Margolis, Alexander J.1
1Department of Mathematics, and Computer Science, Wesleyan University, Science Tower, 265 Church Street, Middletown, CT 06459-0128 (USA)
Annales de l'Institut Fourier, Online first, 34 p.

We show that if $H$ is a commensurated subgroup of $G$ such that both $H$ and $G$ are of type $VFP$ and $\operatorname{vcd}(G)=\operatorname{vcd}(H)+1$, then $G$ is the fundamental group of a graph of groups in which all vertex and edge groups are commensurable to $H$. We also investigate commensurated subgroups of one-relator groups and duality groups.

Nous montrons que si $H$ est un sous-groupe commensuré de $G$ tel que $H$ et $G$ soient tous deux de type $VFP$ et $\operatorname{vcd}(G)=\operatorname{vcd}(H)+1$, alors $G$ est le groupe fondamental d’un graphe de groupes dans lequel tous les groupes de sommets et d’arêtes sont commensurables à $H$. Nous étudions également les sous-groupes commensuré des groupes définis par une seule relation et groupes à dualité.

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DOI : 10.5802/aif.3766
Classification : 20J05, 20E06, 20E08, 20J06, 20F65
Keywords: commensurated subgroup, cohomological dimension, trees, splitting
Mots-clés : sous-groupe commensuré, dimension cohomologique, arbres, scindements

Margolis, Alexander J.  1

1 Department of Mathematics, and Computer Science, Wesleyan University, Science Tower, 265 Church Street, Middletown, CT 06459-0128 (USA) 
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Margolis, Alexander J. Groups of cohomological codimension one. Annales de l'Institut Fourier, Online first, 34 p.

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