Subgroups of direct products of limit groups

Martin R. Bridson (1) , James Howie , Charles F Miller Iii , Hamish Short (2, 3)

1 MI - Mathematical Institute [Oxford]
2 I2M - Institut de Mathématiques de Marseille
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

If $G_1,...,G_n$ are limit groups and $S\subset G_1\times...\times G_n$ is of type $\FP_n(\mathbb Q)$ then $S$ contains a subgroup of finite index that is itself a direct product of at most $n$ limit groups. This settles a question of Sela.

Mots clés: homology of group; limit group; residually-free group; subdirect product

Domaines: Théorie des groupes [math.GR]; Topologie géométrique [math.GT]

Martin R. Bridson, James Howie, Charles F Miller Iii, Hamish Short. Subgroups of direct products of limit groups. Annals of Mathematics, 2007, 170 (3), pp.1446-1467. ⟨10.4007/annals.2009.170.1447⟩. ⟨hal-00821481⟩