The subgroups of direct products of surface groups

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

Preprint, August 2000; now appeared in Geom. Dedicata, vol. 92 (2002), 95--103.

A subgroup of a product of $n$ surface groups is of type $FP_n$ if and only if it contains a subgroup of finite index that is itself a product of (at most $n$) surface groups.