Subgroups of direct products of limit groups


SelaIf $\Gamma_1,\dots,\Gamma_n$ are limit groups and $S\subset\Gamma_1\times\dots\times\Gamma_n$ is of type ${\rm FP}_n(\mathbb Q)$ then $S$ contains a subgroup of finite index that is itself a direct product of at most $n$ limit groups. This answers a question of Sela.


Martin R. Bridson

Mathematical Institute
24-29 St Giles’
Oxford OX1 3LB
United Kingdom

James Howie

Department of Mathematics and Maxwell Institute for Mathematical Sciences
Heriot-Watt University
Edinburgh EH14 4AS
United Kingdom

Charles F. Miller III

Department of Mathematics and Statistics
University of Melbourne
Melbourne 3010

Hamish Short

L.A.T.P., U.M.R. 6632
Centre de Mathématiques et d’Informatique
39 Rue Joliot-Curie
Université de Provence
13453 Marseille cedex 13