Groups, Geometry, and Dynamics

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Volume 4, Issue 4, 2010, pp. 901–908
DOI: 10.4171/GGD/113

Published online: 2010-10-15

Universal diagram groups with identical Poincaré series

Stephen J. Pride[1]

(1) University of Glasgow, UK

For a diagram group G, the first derived quotient G1/G2 is always free abelian (as proved by M. Sapir and V. Guba). However the second derived quotient G2/G3 may contain torsion. In fact, we show that for any finite or countably infinite direct product of cyclic groups A, there is a diagram group with second derived quotient A. We use that to construct families with the properties of the title.

Keywords: Diagram groups, derived quotient, FP-infinity, Poincaré series

Pride Stephen: Universal diagram groups with identical Poincaré series. Groups Geom. Dyn. 4 (2010), 901-908. doi: 10.4171/GGD/113