Subgroups of direct products of limit groups

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

Published 2007-04-30, updated 2007-11-06Version 2

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.