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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.