Subgroups of direct products of limit groups

Bridson, Martin R; Howie, James; Miller III, Charles F; Short, Hamish

Subgroups of direct products of limit groups

Authors

Bridson, Martin R

Howie, James

Miller III, Charles F

Short, Hamish

Description

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.
20 pages, no figures. Final version. Accepted by the Annals of Mathematics