Subgroups of direct products of limit groups

Abstract

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

References in corpus (2)

• Limit groups as limits of free groups: compactifying the set of free groups
• Limit groups are CAT(0)

Cited by in corpus (2)

• Decision problems and profinite completions of groups
• Subgroup separability in residually free groups