Geodesic
Universal diagram groups with identical Poincaré series
Stephen J. Pride1
1University of Glasgow, UK
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 901-908

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DOI

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.
DOI : 10.4171/ggd/113
Classification : 20-XX, 57-XX, 00-XX
Mots-clés : Diagram groups, derived quotient, FP-infinity, Poincaré series

Stephen J. Pride  1

1 University of Glasgow, UK 
Stephen J. Pride. Universal diagram groups with identical Poincaré series. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 901-908. doi: 10.4171/ggd/113
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     title = {Universal diagram groups with identical {Poincar\'e} series},
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     year = {2010},
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     number = {4},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/113/}
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